What is the Greatest Common Factor of 1260 and 1274?

Greatest common factor (GCF) of 1260 and 1274 is 14.

GCF(1260,1274) = 14

We will now calculate the prime factors of 1260 and 1274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1260 and 1274.

How to find the GCF of 1260 and 1274?

We will first find the prime factorization of 1260 and 1274. After we will calculate the factors of 1260 and 1274 and find the biggest common factor number .

Step-1: Prime Factorization of 1260

Prime factors of 1260 are 2, 3, 5, 7. Prime factorization of 1260 in exponential form is:

1260 = 2² × 3² × 5¹ × 7¹

Step-2: Prime Factorization of 1274

Prime factors of 1274 are 2, 7, 13. Prime factorization of 1274 in exponential form is:

1274 = 2¹ × 7² × 13¹

Step-3: Factors of 1260

List of positive integer factors of 1260 that divides 1260 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630

Step-4: Factors of 1274

List of positive integer factors of 1274 that divides 1260 without a remainder.

1, 2, 7, 13, 14, 26, 49, 91, 98, 182, 637

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1260 and 1274. The biggest common factor number is the GCF number.
So the greatest common factor 1260 and 1274 is 14.

Also check out the Least Common Multiple of 1260 and 1274