What is the Greatest Common Factor of 85974 and 85989?

Greatest common factor (GCF) of 85974 and 85989 is 3.

GCF(85974,85989) = 3

We will now calculate the prime factors of 85974 and 85989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85974 and 85989.

How to find the GCF of 85974 and 85989?

We will first find the prime factorization of 85974 and 85989. After we will calculate the factors of 85974 and 85989 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 85989

Prime factors of 85989 are 3, 28663. Prime factorization of 85989 in exponential form is:

85989 = 3¹ × 28663¹

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 85989

List of positive integer factors of 85989 that divides 85974 without a remainder.

1, 3, 28663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85974 and 85989. The biggest common factor number is the GCF number.
So the greatest common factor 85974 and 85989 is 3.

Also check out the Least Common Multiple of 85974 and 85989