What is the Greatest Common Factor of 10 and 470?

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

GCF(10,470) = 10

We will now calculate the prime factors of 10 and 470, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10 and 470.

How to find the GCF of 10 and 470?

We will first find the prime factorization of 10 and 470. After we will calculate the factors of 10 and 470 and find the biggest common factor number .

Step-1: Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:

10 = 2¹ × 5¹

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 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5

Step-4: Factors of 470

List of positive integer factors of 470 that divides 10 without a remainder.

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

Final Step: Biggest Common Factor Number

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

Also check out the Least Common Multiple of 10 and 470