What is the Greatest Common Factor of 1460 and 1476?

Greatest common factor (GCF) of 1460 and 1476 is 4.

GCF(1460,1476) = 4

We will now calculate the prime factors of 1460 and 1476, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1460 and 1476.

How to find the GCF of 1460 and 1476?

We will first find the prime factorization of 1460 and 1476. After we will calculate the factors of 1460 and 1476 and find the biggest common factor number .

Step-1: Prime Factorization of 1460

Prime factors of 1460 are 2, 5, 73. Prime factorization of 1460 in exponential form is:

1460 = 2² × 5¹ × 73¹

Step-2: Prime Factorization of 1476

Prime factors of 1476 are 2, 3, 41. Prime factorization of 1476 in exponential form is:

1476 = 2² × 3² × 41¹

Step-3: Factors of 1460

List of positive integer factors of 1460 that divides 1460 without a remainder.

1, 2, 4, 5, 10, 20, 73, 146, 292, 365, 730

Step-4: Factors of 1476

List of positive integer factors of 1476 that divides 1460 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 41, 82, 123, 164, 246, 369, 492, 738

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1460 and 1476. The biggest common factor number is the GCF number.
So the greatest common factor 1460 and 1476 is 4.

Also check out the Least Common Multiple of 1460 and 1476