What is the Greatest Common Factor of 74971 and 74984?

Greatest common factor (GCF) of 74971 and 74984 is 13.

GCF(74971,74984) = 13

We will now calculate the prime factors of 74971 and 74984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74971 and 74984.

How to find the GCF of 74971 and 74984?

We will first find the prime factorization of 74971 and 74984. After we will calculate the factors of 74971 and 74984 and find the biggest common factor number .

Step-1: Prime Factorization of 74971

Prime factors of 74971 are 13, 73, 79. Prime factorization of 74971 in exponential form is:

74971 = 13¹ × 73¹ × 79¹

Step-2: Prime Factorization of 74984

Prime factors of 74984 are 2, 7, 13, 103. Prime factorization of 74984 in exponential form is:

74984 = 2³ × 7¹ × 13¹ × 103¹

Step-3: Factors of 74971

List of positive integer factors of 74971 that divides 74971 without a remainder.

1, 13, 73, 79, 949, 1027, 5767

Step-4: Factors of 74984

List of positive integer factors of 74984 that divides 74971 without a remainder.

1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 103, 104, 182, 206, 364, 412, 721, 728, 824, 1339, 1442, 2678, 2884, 5356, 5768, 9373, 10712, 18746, 37492

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74971 and 74984. The biggest common factor number is the GCF number.
So the greatest common factor 74971 and 74984 is 13.

Also check out the Least Common Multiple of 74971 and 74984