What is the Greatest Common Factor of 49712 and 49725?

Greatest common factor (GCF) of 49712 and 49725 is 13.

GCF(49712,49725) = 13

We will now calculate the prime factors of 49712 and 49725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49712 and 49725.

How to find the GCF of 49712 and 49725?

We will first find the prime factorization of 49712 and 49725. After we will calculate the factors of 49712 and 49725 and find the biggest common factor number .

Step-1: Prime Factorization of 49712

Prime factors of 49712 are 2, 13, 239. Prime factorization of 49712 in exponential form is:

49712 = 2⁴ × 13¹ × 239¹

Step-2: Prime Factorization of 49725

Prime factors of 49725 are 3, 5, 13, 17. Prime factorization of 49725 in exponential form is:

49725 = 3² × 5² × 13¹ × 17¹

Step-3: Factors of 49712

List of positive integer factors of 49712 that divides 49712 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 208, 239, 478, 956, 1912, 3107, 3824, 6214, 12428, 24856

Step-4: Factors of 49725

List of positive integer factors of 49725 that divides 49712 without a remainder.

1, 3, 5, 9, 13, 15, 17, 25, 39, 45, 51, 65, 75, 85, 117, 153, 195, 221, 225, 255, 325, 425, 585, 663, 765, 975, 1105, 1275, 1989, 2925, 3315, 3825, 5525, 9945, 16575

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49712 and 49725. The biggest common factor number is the GCF number.
So the greatest common factor 49712 and 49725 is 13.

Also check out the Least Common Multiple of 49712 and 49725