What is the Greatest Common Factor of 75460 and 75480?

Greatest common factor (GCF) of 75460 and 75480 is 20.

GCF(75460,75480) = 20

We will now calculate the prime factors of 75460 and 75480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75460 and 75480.

How to find the GCF of 75460 and 75480?

We will first find the prime factorization of 75460 and 75480. After we will calculate the factors of 75460 and 75480 and find the biggest common factor number .

Step-1: Prime Factorization of 75460

Prime factors of 75460 are 2, 5, 7, 11. Prime factorization of 75460 in exponential form is:

75460 = 2² × 5¹ × 7³ × 11¹

Step-2: Prime Factorization of 75480

Prime factors of 75480 are 2, 3, 5, 17, 37. Prime factorization of 75480 in exponential form is:

75480 = 2³ × 3¹ × 5¹ × 17¹ × 37¹

Step-3: Factors of 75460

List of positive integer factors of 75460 that divides 75460 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 49, 55, 70, 77, 98, 110, 140, 154, 196, 220, 245, 308, 343, 385, 490, 539, 686, 770, 980, 1078, 1372, 1540, 1715, 2156, 2695, 3430, 3773, 5390, 6860, 7546, 10780, 15092, 18865, 37730

Step-4: Factors of 75480

List of positive integer factors of 75480 that divides 75460 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 37, 40, 51, 60, 68, 74, 85, 102, 111, 120, 136, 148, 170, 185, 204, 222, 255, 296, 340, 370, 408, 444, 510, 555, 629, 680, 740, 888, 1020, 1110, 1258, 1480, 1887, 2040, 2220, 2516, 3145, 3774, 4440, 5032, 6290, 7548, 9435, 12580, 15096, 18870, 25160, 37740

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75460 and 75480. The biggest common factor number is the GCF number.
So the greatest common factor 75460 and 75480 is 20.

Also check out the Least Common Multiple of 75460 and 75480