What is the Greatest Common Factor of 1460 and 1478?

Greatest common factor (GCF) of 1460 and 1478 is 2.

GCF(1460,1478) = 2

We will now calculate the prime factors of 1460 and 1478, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1460 and 1478.

How to find the GCF of 1460 and 1478?

We will first find the prime factorization of 1460 and 1478. After we will calculate the factors of 1460 and 1478 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 1478

Prime factors of 1478 are 2, 739. Prime factorization of 1478 in exponential form is:

1478 = 2¹ × 739¹

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 1478

List of positive integer factors of 1478 that divides 1460 without a remainder.

1, 2, 739

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1460 and 1478. The biggest common factor number is the GCF number.
So the greatest common factor 1460 and 1478 is 2.

Also check out the Least Common Multiple of 1460 and 1478