What is the Greatest Common Factor of 7560 and 7574?

Greatest common factor (GCF) of 7560 and 7574 is 14.

GCF(7560,7574) = 14

We will now calculate the prime factors of 7560 and 7574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7560 and 7574.

How to find the GCF of 7560 and 7574?

We will first find the prime factorization of 7560 and 7574. After we will calculate the factors of 7560 and 7574 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7574

Prime factors of 7574 are 2, 7, 541. Prime factorization of 7574 in exponential form is:

7574 = 2¹ × 7¹ × 541¹

Step-3: Factors of 7560

List of positive integer factors of 7560 that divides 7560 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

Step-4: Factors of 7574

List of positive integer factors of 7574 that divides 7560 without a remainder.

1, 2, 7, 14, 541, 1082, 3787

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7560 and 7574. The biggest common factor number is the GCF number.
So the greatest common factor 7560 and 7574 is 14.

Also check out the Least Common Multiple of 7560 and 7574