What is the Greatest Common Factor of 74750 and 74760?

Greatest common factor (GCF) of 74750 and 74760 is 10.

GCF(74750,74760) = 10

We will now calculate the prime factors of 74750 and 74760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74750 and 74760.

How to find the GCF of 74750 and 74760?

We will first find the prime factorization of 74750 and 74760. After we will calculate the factors of 74750 and 74760 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 74760

Prime factors of 74760 are 2, 3, 5, 7, 89. Prime factorization of 74760 in exponential form is:

74760 = 2³ × 3¹ × 5¹ × 7¹ × 89¹

Step-3: Factors of 74750

List of positive integer factors of 74750 that divides 74750 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

Step-4: Factors of 74760

List of positive integer factors of 74760 that divides 74750 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 89, 105, 120, 140, 168, 178, 210, 267, 280, 356, 420, 445, 534, 623, 712, 840, 890, 1068, 1246, 1335, 1780, 1869, 2136, 2492, 2670, 3115, 3560, 3738, 4984, 5340, 6230, 7476, 9345, 10680, 12460, 14952, 18690, 24920, 37380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74750 and 74760. The biggest common factor number is the GCF number.
So the greatest common factor 74750 and 74760 is 10.

Also check out the Least Common Multiple of 74750 and 74760