Greatest common divisor(Two numbers)

About the calculation of Greatest common divisor(Two numbers)

Enter the two numbers you want to calculate the greatest common divisor and click "calculate the greatest common divisor", Greatest common divisor of the values entered will be displayed.

It also shows how to find the greatest common factor using prime factorization and how to calculate it using long division.

Please enter an integer between 2 and 10,000,000,000,000,000.

What is the greatest common denominator?

The divisors that two or more integers have in common are called common divisors, and the largest of these is called the greatest common divisor.

For example, suppose you want to find the greatest common factor of 12 and 18.

The divisors of 12 are 1, 2, 3, 4, 6, and 12, and the divisors of 18 are 1, 2, 3, 6, 9, and 18.

Of these divisors, the common ones "1, 2, 3, and 6" are the common divisors of 12 and 18, and the largest of these, 6, is the greatest common divisor of 12 and 18.

How to calculate the greatest common denominator

To calculate the greatest common factor, you can factorize each number into prime numbers, divide by a common prime number, or write out the divisors.

Example: Calculate the greatest common divisor of 36 and 48.

1. How to calculate using prime factorization

Factorize each of them into prime factors.

36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

Write down the common prime factors for each.

Common prime factors: 2, 2, 3

The product of these common prime factors is the greatest common factor.

Therefore, the greatest common factor is 2 × 2 × 3 = 12.

2. How to calculate by long division

Calculate the greatest common factor using long division.

List the numbers you want to calculate the greatest common factor for and write the prime numbers that divide them on the left.

Since it is divisible by 2, write 2 on the left.

2
 
 36 48

Under each number, write the quotient when divided by the number on the left.

Here, we divide each of these by 2 to write 18 and 24.

2
 
 36 48
    18 24

Keep dividing each number until there are no more prime numbers that divide it.

Once you've finished dividing, the greatest common factor will be the number multiplied by the vertical number on the left.

2
 
 36 48
2
 
 18 24
3
 
 9 12
    3 4

Therefore, the greatest common factor is 2 × 2 × 3 = 12.

3. How to write out divisors

Find the divisors of each number and pick out the one with the largest number.

Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Therefore, the greatest common factor is 12.

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