How To Find The Greatest Common Divisor

Welcome to the greatest common divisor or greatest common factor video. So just to be clear, first of all, when someone asks you whether what's the greatest common divisor of 12 and 8? Or they ask you what's the greatest common factor of 12 and 8? That's a c right there for common. I don't know why. How to Find the Greatest Common Factor of Two Numbers. Prime numbers have only two factors: 1 and the number itself. Composite numbers have more factors. Three is a prime number; you can only multiply 1 and 3 to get 3 as the product. By contrast, 12 is a composite number with factors of: 1 and 12; 2 and 6; and 3 and 4. The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

  1. How To Find Greatest Common Divisor In C Programming
  2. Find Divisors Of A Number
  3. How To Find The Greatest Common Divisor Of Two Numbers
  • About GCD and LCM. GCD stands for Greatest Common Divisor. GCD is largest number that divides the given numbers. Find the GCD of 45 and 54. Step 1: Find the divisiors of given numbers: The divisiors of 45 are: 1, 3, 5, 9, 15, 45 The divisiors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54 Step 2: Find the greatest number that these two lists share in common.
  • GCD and LCM calculator. This calculator will find Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two or more numbers. Step-by-step explanation is provided. GCD and LCM Calculator. Enter a list of positive integer numbers, separated by spaces or commas.
  • Greatest common divisor. In mathematics, the greatest common divisor ( gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. The greatest common divisor is also known as the greatest common factor ( gcf ).

The greatest common factor (GCF) of a set of numbers is the largest number that’s a factor of every number in that set. Finding the GCF is helpful when you want to reduce a fraction to its lowest terms.

You can find the GCF in two ways. The first option is to list all the factor pairs of the numbers and choose the largest factor that appears in both (or all) the lists.

The other method uses prime factors, which I discuss in the preceding section. Here’s how to find the GCF:

How To Find Greatest Common Divisor In C Programming

  1. Decompose the numbers into their prime factors.

  2. Underline the factors that all the original numbers have in common.

  3. Multiply the underlined numbers to get the GCF.

Find Divisors Of A Number

Sample questions

  1. Find the greatest common factor of 12 and 20.

    4. Write down all the factor pairs of 12 and 20:

    Factor pairs of 12: 1 x 12, 2 x 6, 3 x 4

    Factor pairs of 20: 1 x 20, 2 x 10, 4 x 5

    The number 4 is the greatest number that appears in both lists of factor pairs, so it’s the GCF.

  2. Find the greatest common factor of 24, 36, and 42.

    6. Decompose all three numbers down to their prime factors:

    24 = 2 x 2 x 2 x 3

    36 = 2 x 2 x 3 x 3

    42 = 2 x 3 x 7

    Underline all factors that are common to all three numbers:

    24 = 2 x 2 x 2 x 3

    36 = 2 x 2 x 3 x 3

    42 = 2 x 3 x 7

    Multiply those underlined numbers to get your answer:

    2 x 3 = 6

Practice questions

  1. Find the greatest common factor of 10 and 22.

  2. What’s the GCF of 8 and 32?

  3. Find the GCF of 30 and 45.

  4. Figure out the GCF of 27 and 72.

  5. Find the GCF of 15, 20, and 35.

  6. Figure out the GCF of 44, 56, and 72.

Following are the answers to the practice questions:

How to find the greatest common divisor of two numbers

How To Find The Greatest Common Divisor Of Two Numbers

  1. The GCF of 10 and 22 is 2.

    Write down all the factor pairs of 10 and 22:

    10: 1 x 10, 2 x 5

    22: 1 x 22, 2 x 11

    The number 2 is the greatest number that appears on both lists.

  2. The GCF of 8 and 32 is 8.

    Write down all the factor pairs of 8 and 32:

    8: 1 x 8, 2 x 4

    32: 1 x 32, 2 x 16, 4 x 8

    The greatest number that appears on both lists is 8.

  3. The GCF of 30 and 45 is 15.

    Write down all the factor pairs of 30 and 45:

    30: 1 x 30, 2 x 15, 3 x 10, 5 x 6

    45: 1 x 45, 3 x 15, 5 x 9

    The greatest number that appears on both lists is 15.

  4. The GCF of 27 and 72 is 9.

    Decompose 27 and 72 into their prime factors and underline every factor that’s common to both:

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    27 = 3 x 3 x 3

    72 = 2 x 2 x 2 x 3 x 3

    Multiply those underlined numbers to get your answer: 3 x 3 = 9.

  5. The GCF of 15, 20, and 35 is 5.

    Decompose the three numbers into their prime factors and underline every factor that’s common to all three:

    15 = 3 x 5

    20 = 2 x 2 x 5

    35 = 5 x 7

    The only factor common to all three numbers is 5.

  6. The GCF of 44, 56, and 72 is 4.

    Decompose all three numbers to their prime factors and underline each factor that’s common to all three:

    44 = 2 x 2 x 11

    56 = 2 x 2 x 2 x 7

    72 = 2 x 2 x 2 x 3 x 3

    Multiply those underlined numbers to get your answer: 2 x 2 = 4.

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