What is the Greatest Common Factor of 85731 and 85749?

Greatest common factor (GCF) of 85731 and 85749 is 3.

GCF(85731,85749) = 3

We will now calculate the prime factors of 85731 and 85749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85731 and 85749.

How to find the GCF of 85731 and 85749?

We will first find the prime factorization of 85731 and 85749. After we will calculate the factors of 85731 and 85749 and find the biggest common factor number .

Step-1: Prime Factorization of 85731

Prime factors of 85731 are 3, 17, 41. Prime factorization of 85731 in exponential form is:

85731 = 3¹ × 17¹ × 41²

Step-2: 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-3: Factors of 85731

List of positive integer factors of 85731 that divides 85731 without a remainder.

1, 3, 17, 41, 51, 123, 697, 1681, 2091, 5043, 28577

Step-4: Factors of 85749

List of positive integer factors of 85749 that divides 85731 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85731 and 85749. The biggest common factor number is the GCF number.
So the greatest common factor 85731 and 85749 is 3.

Also check out the Least Common Multiple of 85731 and 85749