What is the Greatest Common Factor of 85974 and 85988?

Greatest common factor (GCF) of 85974 and 85988 is 14.

GCF(85974,85988) = 14

We will now calculate the prime factors of 85974 and 85988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85974 and 85988.

How to find the GCF of 85974 and 85988?

We will first find the prime factorization of 85974 and 85988. After we will calculate the factors of 85974 and 85988 and find the biggest common factor number .

Step-1: Prime Factorization of 85974

Prime factors of 85974 are 2, 3, 7, 23, 89. Prime factorization of 85974 in exponential form is:

85974 = 2¹ × 3¹ × 7¹ × 23¹ × 89¹

Step-2: Prime Factorization of 85988

Prime factors of 85988 are 2, 7, 37, 83. Prime factorization of 85988 in exponential form is:

85988 = 2² × 7¹ × 37¹ × 83¹

Step-3: Factors of 85974

List of positive integer factors of 85974 that divides 85974 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 89, 138, 161, 178, 267, 322, 483, 534, 623, 966, 1246, 1869, 2047, 3738, 4094, 6141, 12282, 14329, 28658, 42987

Step-4: Factors of 85988

List of positive integer factors of 85988 that divides 85974 without a remainder.

1, 2, 4, 7, 14, 28, 37, 74, 83, 148, 166, 259, 332, 518, 581, 1036, 1162, 2324, 3071, 6142, 12284, 21497, 42994

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85974 and 85988. The biggest common factor number is the GCF number.
So the greatest common factor 85974 and 85988 is 14.

Also check out the Least Common Multiple of 85974 and 85988