What is the Greatest Common Factor of 74475 and 74480?

Greatest common factor (GCF) of 74475 and 74480 is 5.

GCF(74475,74480) = 5

We will now calculate the prime factors of 74475 and 74480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74475 and 74480.

How to find the GCF of 74475 and 74480?

We will first find the prime factorization of 74475 and 74480. After we will calculate the factors of 74475 and 74480 and find the biggest common factor number .

Step-1: Prime Factorization of 74475

Prime factors of 74475 are 3, 5, 331. Prime factorization of 74475 in exponential form is:

74475 = 3² × 5² × 331¹

Step-2: Prime Factorization of 74480

Prime factors of 74480 are 2, 5, 7, 19. Prime factorization of 74480 in exponential form is:

74480 = 2⁴ × 5¹ × 7² × 19¹

Step-3: Factors of 74475

List of positive integer factors of 74475 that divides 74475 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 331, 993, 1655, 2979, 4965, 8275, 14895, 24825

Step-4: Factors of 74480

List of positive integer factors of 74480 that divides 74475 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 19, 20, 28, 35, 38, 40, 49, 56, 70, 76, 80, 95, 98, 112, 133, 140, 152, 190, 196, 245, 266, 280, 304, 380, 392, 490, 532, 560, 665, 760, 784, 931, 980, 1064, 1330, 1520, 1862, 1960, 2128, 2660, 3724, 3920, 4655, 5320, 7448, 9310, 10640, 14896, 18620, 37240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74475 and 74480. The biggest common factor number is the GCF number.
So the greatest common factor 74475 and 74480 is 5.

Also check out the Least Common Multiple of 74475 and 74480