What is the Greatest Common Factor of 460 and 470?

Greatest common factor (GCF) of 460 and 470 is 10.

GCF(460,470) = 10

We will now calculate the prime factors of 460 and 470, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 460 and 470.

How to find the GCF of 460 and 470?

We will first find the prime factorization of 460 and 470. After we will calculate the factors of 460 and 470 and find the biggest common factor number .

Step-1: Prime Factorization of 460

Prime factors of 460 are 2, 5, 23. Prime factorization of 460 in exponential form is:

460 = 2² × 5¹ × 23¹

Step-2: Prime Factorization of 470

Prime factors of 470 are 2, 5, 47. Prime factorization of 470 in exponential form is:

470 = 2¹ × 5¹ × 47¹

Step-3: Factors of 460

List of positive integer factors of 460 that divides 460 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230

Step-4: Factors of 470

List of positive integer factors of 470 that divides 460 without a remainder.

1, 2, 5, 10, 47, 94, 235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 460 and 470. The biggest common factor number is the GCF number.
So the greatest common factor 460 and 470 is 10.

Also check out the Least Common Multiple of 460 and 470