What is the Greatest Common Factor of 31754 and 31768?

Greatest common factor (GCF) of 31754 and 31768 is 2.

GCF(31754,31768) = 2

We will now calculate the prime factors of 31754 and 31768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31754 and 31768.

How to find the GCF of 31754 and 31768?

We will first find the prime factorization of 31754 and 31768. After we will calculate the factors of 31754 and 31768 and find the biggest common factor number .

Step-1: Prime Factorization of 31754

Prime factors of 31754 are 2, 15877. Prime factorization of 31754 in exponential form is:

31754 = 2¹ × 15877¹

Step-2: Prime Factorization of 31768

Prime factors of 31768 are 2, 11, 19. Prime factorization of 31768 in exponential form is:

31768 = 2³ × 11¹ × 19²

Step-3: Factors of 31754

List of positive integer factors of 31754 that divides 31754 without a remainder.

1, 2, 15877

Step-4: Factors of 31768

List of positive integer factors of 31768 that divides 31754 without a remainder.

1, 2, 4, 8, 11, 19, 22, 38, 44, 76, 88, 152, 209, 361, 418, 722, 836, 1444, 1672, 2888, 3971, 7942, 15884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31754 and 31768. The biggest common factor number is the GCF number.
So the greatest common factor 31754 and 31768 is 2.

Also check out the Least Common Multiple of 31754 and 31768