What is the Greatest Common Factor of 75460 and 75465?

Greatest common factor (GCF) of 75460 and 75465 is 5.

GCF(75460,75465) = 5

We will now calculate the prime factors of 75460 and 75465, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75460 and 75465.

How to find the GCF of 75460 and 75465?

We will first find the prime factorization of 75460 and 75465. After we will calculate the factors of 75460 and 75465 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 75465

Prime factors of 75465 are 3, 5, 13, 43. Prime factorization of 75465 in exponential form is:

75465 = 3³ × 5¹ × 13¹ × 43¹

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 75465

List of positive integer factors of 75465 that divides 75460 without a remainder.

1, 3, 5, 9, 13, 15, 27, 39, 43, 45, 65, 117, 129, 135, 195, 215, 351, 387, 559, 585, 645, 1161, 1677, 1755, 1935, 2795, 5031, 5805, 8385, 15093, 25155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75460 and 75465. The biggest common factor number is the GCF number.
So the greatest common factor 75460 and 75465 is 5.

Also check out the Least Common Multiple of 75460 and 75465