What is the Greatest Common Factor of 49725 and 49742?

Greatest common factor (GCF) of 49725 and 49742 is 17.

GCF(49725,49742) = 17

We will now calculate the prime factors of 49725 and 49742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49725 and 49742.

How to find the GCF of 49725 and 49742?

We will first find the prime factorization of 49725 and 49742. After we will calculate the factors of 49725 and 49742 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 49742

Prime factors of 49742 are 2, 7, 11, 17, 19. Prime factorization of 49742 in exponential form is:

49742 = 2¹ × 7¹ × 11¹ × 17¹ × 19¹

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 49742

List of positive integer factors of 49742 that divides 49725 without a remainder.

1, 2, 7, 11, 14, 17, 19, 22, 34, 38, 77, 119, 133, 154, 187, 209, 238, 266, 323, 374, 418, 646, 1309, 1463, 2261, 2618, 2926, 3553, 4522, 7106, 24871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49725 and 49742. The biggest common factor number is the GCF number.
So the greatest common factor 49725 and 49742 is 17.

Also check out the Least Common Multiple of 49725 and 49742