What is the Greatest Common Factor of 47712 and 47724?

Greatest common factor (GCF) of 47712 and 47724 is 12.

GCF(47712,47724) = 12

We will now calculate the prime factors of 47712 and 47724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47712 and 47724.

How to find the GCF of 47712 and 47724?

We will first find the prime factorization of 47712 and 47724. After we will calculate the factors of 47712 and 47724 and find the biggest common factor number .

Step-1: Prime Factorization of 47712

Prime factors of 47712 are 2, 3, 7, 71. Prime factorization of 47712 in exponential form is:

47712 = 2⁵ × 3¹ × 7¹ × 71¹

Step-2: Prime Factorization of 47724

Prime factors of 47724 are 2, 3, 41, 97. Prime factorization of 47724 in exponential form is:

47724 = 2² × 3¹ × 41¹ × 97¹

Step-3: Factors of 47712

List of positive integer factors of 47712 that divides 47712 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 71, 84, 96, 112, 142, 168, 213, 224, 284, 336, 426, 497, 568, 672, 852, 994, 1136, 1491, 1704, 1988, 2272, 2982, 3408, 3976, 5964, 6816, 7952, 11928, 15904, 23856

Step-4: Factors of 47724

List of positive integer factors of 47724 that divides 47712 without a remainder.

1, 2, 3, 4, 6, 12, 41, 82, 97, 123, 164, 194, 246, 291, 388, 492, 582, 1164, 3977, 7954, 11931, 15908, 23862

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47712 and 47724. The biggest common factor number is the GCF number.
So the greatest common factor 47712 and 47724 is 12.

Also check out the Least Common Multiple of 47712 and 47724