What is the Greatest Common Factor of 5460 and 5474?

Greatest common factor (GCF) of 5460 and 5474 is 14.

GCF(5460,5474) = 14

We will now calculate the prime factors of 5460 and 5474, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5460 and 5474.

How to find the GCF of 5460 and 5474?

We will first find the prime factorization of 5460 and 5474. After we will calculate the factors of 5460 and 5474 and find the biggest common factor number .

Step-1: Prime Factorization of 5460

Prime factors of 5460 are 2, 3, 5, 7, 13. Prime factorization of 5460 in exponential form is:

5460 = 2² × 3¹ × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 5474

Prime factors of 5474 are 2, 7, 17, 23. Prime factorization of 5474 in exponential form is:

5474 = 2¹ × 7¹ × 17¹ × 23¹

Step-3: Factors of 5460

List of positive integer factors of 5460 that divides 5460 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730

Step-4: Factors of 5474

List of positive integer factors of 5474 that divides 5460 without a remainder.

1, 2, 7, 14, 17, 23, 34, 46, 119, 161, 238, 322, 391, 782, 2737

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5460 and 5474. The biggest common factor number is the GCF number.
So the greatest common factor 5460 and 5474 is 14.

Also check out the Least Common Multiple of 5460 and 5474