What is the Greatest Common Factor of 1470 and 1490?

Greatest common factor (GCF) of 1470 and 1490 is 10.

GCF(1470,1490) = 10

We will now calculate the prime factors of 1470 and 1490, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1470 and 1490.

How to find the GCF of 1470 and 1490?

We will first find the prime factorization of 1470 and 1490. After we will calculate the factors of 1470 and 1490 and find the biggest common factor number .

Step-1: Prime Factorization of 1470

Prime factors of 1470 are 2, 3, 5, 7. Prime factorization of 1470 in exponential form is:

1470 = 2¹ × 3¹ × 5¹ × 7²

Step-2: Prime Factorization of 1490

Prime factors of 1490 are 2, 5, 149. Prime factorization of 1490 in exponential form is:

1490 = 2¹ × 5¹ × 149¹

Step-3: Factors of 1470

List of positive integer factors of 1470 that divides 1470 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735

Step-4: Factors of 1490

List of positive integer factors of 1490 that divides 1470 without a remainder.

1, 2, 5, 10, 149, 298, 745

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1470 and 1490. The biggest common factor number is the GCF number.
So the greatest common factor 1470 and 1490 is 10.

Also check out the Least Common Multiple of 1470 and 1490