What is the Greatest Common Factor of 74760 and 74775?

Greatest common factor (GCF) of 74760 and 74775 is 15.

GCF(74760,74775) = 15

We will now calculate the prime factors of 74760 and 74775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74760 and 74775.

How to find the GCF of 74760 and 74775?

We will first find the prime factorization of 74760 and 74775. After we will calculate the factors of 74760 and 74775 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 74775

Prime factors of 74775 are 3, 5, 997. Prime factorization of 74775 in exponential form is:

74775 = 3¹ × 5² × 997¹

Step-3: Factors of 74760

List of positive integer factors of 74760 that divides 74760 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

Step-4: Factors of 74775

List of positive integer factors of 74775 that divides 74760 without a remainder.

1, 3, 5, 15, 25, 75, 997, 2991, 4985, 14955, 24925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74760 and 74775. The biggest common factor number is the GCF number.
So the greatest common factor 74760 and 74775 is 15.

Also check out the Least Common Multiple of 74760 and 74775