What is the Greatest Common Factor of 85724 and 85740?

Greatest common factor (GCF) of 85724 and 85740 is 4.

GCF(85724,85740) = 4

We will now calculate the prime factors of 85724 and 85740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85724 and 85740.

How to find the GCF of 85724 and 85740?

We will first find the prime factorization of 85724 and 85740. After we will calculate the factors of 85724 and 85740 and find the biggest common factor number .

Step-1: Prime Factorization of 85724

Prime factors of 85724 are 2, 29, 739. Prime factorization of 85724 in exponential form is:

85724 = 2² × 29¹ × 739¹

Step-2: Prime Factorization of 85740

Prime factors of 85740 are 2, 3, 5, 1429. Prime factorization of 85740 in exponential form is:

85740 = 2² × 3¹ × 5¹ × 1429¹

Step-3: Factors of 85724

List of positive integer factors of 85724 that divides 85724 without a remainder.

1, 2, 4, 29, 58, 116, 739, 1478, 2956, 21431, 42862

Step-4: Factors of 85740

List of positive integer factors of 85740 that divides 85724 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1429, 2858, 4287, 5716, 7145, 8574, 14290, 17148, 21435, 28580, 42870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85724 and 85740. The biggest common factor number is the GCF number.
So the greatest common factor 85724 and 85740 is 4.

Also check out the Least Common Multiple of 85724 and 85740