What is the Greatest Common Factor of 85749 and 85764?

Greatest common factor (GCF) of 85749 and 85764 is 3.

GCF(85749,85764) = 3

We will now calculate the prime factors of 85749 and 85764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85749 and 85764.

How to find the GCF of 85749 and 85764?

We will first find the prime factorization of 85749 and 85764. After we will calculate the factors of 85749 and 85764 and find the biggest common factor number .

Step-1: Prime Factorization of 85749

Prime factors of 85749 are 3, 101, 283. Prime factorization of 85749 in exponential form is:

85749 = 3¹ × 101¹ × 283¹

Step-2: Prime Factorization of 85764

Prime factors of 85764 are 2, 3, 7, 1021. Prime factorization of 85764 in exponential form is:

85764 = 2² × 3¹ × 7¹ × 1021¹

Step-3: Factors of 85749

List of positive integer factors of 85749 that divides 85749 without a remainder.

1, 3, 101, 283, 303, 849, 28583

Step-4: Factors of 85764

List of positive integer factors of 85764 that divides 85749 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 1021, 2042, 3063, 4084, 6126, 7147, 12252, 14294, 21441, 28588, 42882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85749 and 85764. The biggest common factor number is the GCF number.
So the greatest common factor 85749 and 85764 is 3.

Also check out the Least Common Multiple of 85749 and 85764