What is the Greatest Common Factor of 7540 and 7560?

Greatest common factor (GCF) of 7540 and 7560 is 20.

GCF(7540,7560) = 20

We will now calculate the prime factors of 7540 and 7560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7540 and 7560.

How to find the GCF of 7540 and 7560?

We will first find the prime factorization of 7540 and 7560. After we will calculate the factors of 7540 and 7560 and find the biggest common factor number .

Step-1: Prime Factorization of 7540

Prime factors of 7540 are 2, 5, 13, 29. Prime factorization of 7540 in exponential form is:

7540 = 2² × 5¹ × 13¹ × 29¹

Step-2: Prime Factorization of 7560

Prime factors of 7560 are 2, 3, 5, 7. Prime factorization of 7560 in exponential form is:

7560 = 2³ × 3³ × 5¹ × 7¹

Step-3: Factors of 7540

List of positive integer factors of 7540 that divides 7540 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 29, 52, 58, 65, 116, 130, 145, 260, 290, 377, 580, 754, 1508, 1885, 3770

Step-4: Factors of 7560

List of positive integer factors of 7560 that divides 7540 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 54, 56, 60, 63, 70, 72, 84, 90, 105, 108, 120, 126, 135, 140, 168, 180, 189, 210, 216, 252, 270, 280, 315, 360, 378, 420, 504, 540, 630, 756, 840, 945, 1080, 1260, 1512, 1890, 2520, 3780

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7540 and 7560. The biggest common factor number is the GCF number.
So the greatest common factor 7540 and 7560 is 20.

Also check out the Least Common Multiple of 7540 and 7560