What is the Greatest Common Factor of 49725 and 49734?

Greatest common factor (GCF) of 49725 and 49734 is 9.

GCF(49725,49734) = 9

We will now calculate the prime factors of 49725 and 49734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49725 and 49734.

How to find the GCF of 49725 and 49734?

We will first find the prime factorization of 49725 and 49734. After we will calculate the factors of 49725 and 49734 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 49734

Prime factors of 49734 are 2, 3, 307. Prime factorization of 49734 in exponential form is:

49734 = 2¹ × 3⁴ × 307¹

Step-3: Factors of 49725

List of positive integer factors of 49725 that divides 49725 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

Step-4: Factors of 49734

List of positive integer factors of 49734 that divides 49725 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 307, 614, 921, 1842, 2763, 5526, 8289, 16578, 24867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49725 and 49734. The biggest common factor number is the GCF number.
So the greatest common factor 49725 and 49734 is 9.

Also check out the Least Common Multiple of 49725 and 49734