Greatest Common Divisor definition (dave hook)

The greatest common divisor of 2 or more without zero integers, is the biggest +ve integer that is divide the all numbers lacking a remainder The another name of the greatest common divisor is the greatest factor(gcf), greatest common denominator, highest common divisor. For example greatest common divisor of 8 and 12 is 4.Now we see about the Greatest common divisor definition.

Greatest common divisor definition Examples:

Greatest common divisor definition Example 1:

Find the greatest common divisor of given numbers 48, 180

Solution:

48 is written by 48 = 2 x 2 x 2 x 2 x 3

180 is written by 180 = 2 ? 2 ? 3 ? 3 ? 5.

Therefore the greatest common divisor = 2 x 2 x 3 = 12

Greatest common divisor definition Example 2:

Find the greatest common divisor of given numbers 21, 15

Solution:

21 is written by 21 = 3 x 7

15 is written by 15 = 3 x 5

Therefore the greatest common divisor = 3

Greatest common divisor definition Example 3:

Find the greatest common divisor of given numbers 15, 21, 18

Solution:

15 is written by 15 = 3 x 5

21 is written by 21 = 3 x 7

18 is written by 18 = 3 x 3 x 2

Therefore the greatest common divisor = 3

Greatest common divisor definition Example 4:

Find the greatest common divisor of given numbers 15, 21

Solution:

15 is written by 15 = 3 x 5

21 is written by 21 = 3 x 7

Therefore the greatest common divisor = 3

Greatest common divisor definition More Examples:

Greatest common divisor definition Example 1:

Find the greatest common divisor of given numbers 25, 65

Solution:

25 is written by 25 = 5 x 5

65 is written by 65 = 5 x 13

Therefore the greatest common divisor = 5

Greatest common divisor definition Example 2:

Find the greatest common divisor of given numbers 8, 64, 128

Solution:

8 is written by 8 = 2 x 2 x 2

64 is written by 64 = 2 x 2 x 2 x 2 x 2 x 2

128 is written by 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Therefore the greatest common divisor = 2 x 2 x 2 = 8

Greatest common divisor definition Example 3:

Find the greatest common divisor of given numbers 8, 18

Solution:

8 is written by 8 = 2 x 2 x 2

18 is written by 18 = 2 ? 3 ? 3.

Therefore the greatest common divisor = 2

Preparation for greatest common factor - example problems.

here we are going to prepare some example problems for gcf

Preparation example: 1

Find the greatest common denominator for 18, 16 using prime factorization method.

Solution:

First we have to find the prime factor for each number

Prime factor for 18 = 2, 3, 3

Prime factor for 16 = 2, 2, 2, 2

Here the common terms for both = 2

Therefore the gcf of given number is = 2

Preparation example: 2

Find the greatest common factor for 55,121

Solution:

First we have to find the prime factors for each

Prime factor for 55 = 5, 11

Prime factor for 121 = 11,11

Here the common term = 11

Therefore the gcf of 55, 121 = 11

Preparation for greatest common factor - example: 3

Preparation example: 3

Find the greatest common factor for 48, 124, and 76

Solution:

First we have to find the prime factor for each one

Prime factor for 48 = 2, 2, 2, 2, 3

Prime factor for 124 = 2,2, 31

Prime factor for 76 = 2,2,19

Here the common factor is 2, 2

Therefore the gcf of given number is 2 * 2 = 4

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Most Common Number System (Nandan Nayak)

Introduction to most common number system:

In this we have most common number system. Most common system in math includes rational system, decimal numbers, fractional number, whole number, and so on. In this topic we will see some example problems for decimal number, fractional numbers, whole numbers, and so on. And also we have practice problems. Let us start to study about most common number system.

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 1: Crystal is creating potpourri bowls using 18 bags of shredded bark and 15 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Crystal can create?

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

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Most Common Number System (Nandan Nayak)

Introduction to most common number system:

In this we have most common number system. Most common system in math includes rational system, decimal numbers, fractional number, whole number, and so on. In this topic we will see some example problems for decimal number, fractional numbers, whole numbers, and so on. And also we have practice problems. Let us start to study about most common number system.

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 1: Crystal is creating potpourri bowls using 18 bags of shredded bark and 15 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Crystal can create?

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

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Greatest Common Divisor definition (dave hook)

The greatest common divisor of 2 or more without zero integers, is the biggest +ve integer that is divide the all numbers lacking a remainder The another name of the greatest common divisor is the greatest factor(gcf), greatest common denominator, highest common divisor. For example greatest common divisor of 8 and 12 is 4.Now we see about the Greatest common divisor definition.

Greatest common divisor definition Examples:

Greatest common divisor definition Example 1:

Find the greatest common divisor of given numbers 48, 180

Solution:

48 is written by 48 = 2 x 2 x 2 x 2 x 3

180 is written by 180 = 2 ? 2 ? 3 ? 3 ? 5.

Therefore the greatest common divisor = 2 x 2 x 3 = 12

Greatest common divisor definition Example 2:

Find the greatest common divisor of given numbers 21, 15

Solution:

21 is written by 21 = 3 x 7

15 is written by 15 = 3 x 5

Therefore the greatest common divisor = 3

Greatest common divisor definition Example 3:

Find the greatest common divisor of given numbers 15, 21, 18

Solution:

15 is written by 15 = 3 x 5

21 is written by 21 = 3 x 7

18 is written by 18 = 3 x 3 x 2

Therefore the greatest common divisor = 3

Greatest common divisor definition Example 4:

Find the greatest common divisor of given numbers 15, 21

Solution:

15 is written by 15 = 3 x 5

21 is written by 21 = 3 x 7

Therefore the greatest common divisor = 3

Greatest common divisor definition More Examples:

Greatest common divisor definition Example 1:

Find the greatest common divisor of given numbers 25, 65

Solution:

25 is written by 25 = 5 x 5

65 is written by 65 = 5 x 13

Therefore the greatest common divisor = 5

Greatest common divisor definition Example 2:

Find the greatest common divisor of given numbers 8, 64, 128

Solution:

8 is written by 8 = 2 x 2 x 2

64 is written by 64 = 2 x 2 x 2 x 2 x 2 x 2

128 is written by 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Therefore the greatest common divisor = 2 x 2 x 2 = 8

Greatest common divisor definition Example 3:

Find the greatest common divisor of given numbers 8, 18

Solution:

8 is written by 8 = 2 x 2 x 2

18 is written by 18 = 2 ? 3 ? 3.

Therefore the greatest common divisor = 2

Preparation for greatest common factor - example problems.

here we are going to prepare some example problems for gcf

Preparation example: 1

Find the greatest common denominator for 18, 16 using prime factorization method.

Solution:

First we have to find the prime factor for each number

Prime factor for 18 = 2, 3, 3

Prime factor for 16 = 2, 2, 2, 2

Here the common terms for both = 2

Therefore the gcf of given number is = 2

Preparation example: 2

Find the greatest common factor for 55,121

Solution:

First we have to find the prime factors for each

Prime factor for 55 = 5, 11

Prime factor for 121 = 11,11

Here the common term = 11

Therefore the gcf of 55, 121 = 11

Preparation for greatest common factor - example: 3

Preparation example: 3

Find the greatest common factor for 48, 124, and 76

Solution:

First we have to find the prime factor for each one

Prime factor for 48 = 2, 2, 2, 2, 3

Prime factor for 124 = 2,2, 31

Prime factor for 76 = 2,2,19

Here the common factor is 2, 2

Therefore the gcf of given number is 2 * 2 = 4

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