What is the Greatest Common Factor of 1450 and 1460?

Greatest common factor (GCF) of 1450 and 1460 is 10.

GCF(1450,1460) = 10

We will now calculate the prime factors of 1450 and 1460, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1450 and 1460.

How to find the GCF of 1450 and 1460?

We will first find the prime factorization of 1450 and 1460. After we will calculate the factors of 1450 and 1460 and find the biggest common factor number .

Step-1: Prime Factorization of 1450

Prime factors of 1450 are 2, 5, 29. Prime factorization of 1450 in exponential form is:

1450 = 2¹ × 5² × 29¹

Step-2: 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-3: Factors of 1450

List of positive integer factors of 1450 that divides 1450 without a remainder.

1, 2, 5, 10, 25, 29, 50, 58, 145, 290, 725

Step-4: Factors of 1460

List of positive integer factors of 1460 that divides 1450 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1450 and 1460. The biggest common factor number is the GCF number.
So the greatest common factor 1450 and 1460 is 10.

Also check out the Least Common Multiple of 1450 and 1460