What is the Greatest Common Factor of 85965 and 85974?

Greatest common factor (GCF) of 85965 and 85974 is 3.

GCF(85965,85974) = 3

We will now calculate the prime factors of 85965 and 85974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85965 and 85974.

How to find the GCF of 85965 and 85974?

We will first find the prime factorization of 85965 and 85974. After we will calculate the factors of 85965 and 85974 and find the biggest common factor number .

Step-1: Prime Factorization of 85965

Prime factors of 85965 are 3, 5, 11, 521. Prime factorization of 85965 in exponential form is:

85965 = 3¹ × 5¹ × 11¹ × 521¹

Step-2: 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-3: Factors of 85965

List of positive integer factors of 85965 that divides 85965 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 521, 1563, 2605, 5731, 7815, 17193, 28655

Step-4: Factors of 85974

List of positive integer factors of 85974 that divides 85965 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85965 and 85974. The biggest common factor number is the GCF number.
So the greatest common factor 85965 and 85974 is 3.

Also check out the Least Common Multiple of 85965 and 85974