What is the Greatest Common Factor of 4560 and 4575?

Greatest common factor (GCF) of 4560 and 4575 is 15.

GCF(4560,4575) = 15

We will now calculate the prime factors of 4560 and 4575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 4560 and 4575.

How to find the GCF of 4560 and 4575?

We will first find the prime factorization of 4560 and 4575. After we will calculate the factors of 4560 and 4575 and find the biggest common factor number .

Step-1: Prime Factorization of 4560

Prime factors of 4560 are 2, 3, 5, 19. Prime factorization of 4560 in exponential form is:

4560 = 2⁴ × 3¹ × 5¹ × 19¹

Step-2: Prime Factorization of 4575

Prime factors of 4575 are 3, 5, 61. Prime factorization of 4575 in exponential form is:

4575 = 3¹ × 5² × 61¹

Step-3: Factors of 4560

List of positive integer factors of 4560 that divides 4560 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 38, 40, 48, 57, 60, 76, 80, 95, 114, 120, 152, 190, 228, 240, 285, 304, 380, 456, 570, 760, 912, 1140, 1520, 2280

Step-4: Factors of 4575

List of positive integer factors of 4575 that divides 4560 without a remainder.

1, 3, 5, 15, 25, 61, 75, 183, 305, 915, 1525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 4560 and 4575. The biggest common factor number is the GCF number.
So the greatest common factor 4560 and 4575 is 15.

Also check out the Least Common Multiple of 4560 and 4575