What is the Greatest Common Factor of 74730 and 74750?

Greatest common factor (GCF) of 74730 and 74750 is 10.

GCF(74730,74750) = 10

We will now calculate the prime factors of 74730 and 74750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74730 and 74750.

How to find the GCF of 74730 and 74750?

We will first find the prime factorization of 74730 and 74750. After we will calculate the factors of 74730 and 74750 and find the biggest common factor number .

Step-1: Prime Factorization of 74730

Prime factors of 74730 are 2, 3, 5, 47, 53. Prime factorization of 74730 in exponential form is:

74730 = 2¹ × 3¹ × 5¹ × 47¹ × 53¹

Step-2: Prime Factorization of 74750

Prime factors of 74750 are 2, 5, 13, 23. Prime factorization of 74750 in exponential form is:

74750 = 2¹ × 5³ × 13¹ × 23¹

Step-3: Factors of 74730

List of positive integer factors of 74730 that divides 74730 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 47, 53, 94, 106, 141, 159, 235, 265, 282, 318, 470, 530, 705, 795, 1410, 1590, 2491, 4982, 7473, 12455, 14946, 24910, 37365

Step-4: Factors of 74750

List of positive integer factors of 74750 that divides 74730 without a remainder.

1, 2, 5, 10, 13, 23, 25, 26, 46, 50, 65, 115, 125, 130, 230, 250, 299, 325, 575, 598, 650, 1150, 1495, 1625, 2875, 2990, 3250, 5750, 7475, 14950, 37375

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74730 and 74750. The biggest common factor number is the GCF number.
So the greatest common factor 74730 and 74750 is 10.

Also check out the Least Common Multiple of 74730 and 74750