What is the Greatest Common Factor of 470 and 490?

Greatest common factor (GCF) of 470 and 490 is 10.

GCF(470,490) = 10

We will now calculate the prime factors of 470 and 490, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 470 and 490.

How to find the GCF of 470 and 490?

We will first find the prime factorization of 470 and 490. After we will calculate the factors of 470 and 490 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 490

Prime factors of 490 are 2, 5, 7. Prime factorization of 490 in exponential form is:

490 = 2¹ × 5¹ × 7²

Step-3: Factors of 470

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

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

Step-4: Factors of 490

List of positive integer factors of 490 that divides 470 without a remainder.

1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 470 and 490. The biggest common factor number is the GCF number.
So the greatest common factor 470 and 490 is 10.

Also check out the Least Common Multiple of 470 and 490