What is the Greatest Common Factor of 1450 and 1470?

Greatest common factor (GCF) of 1450 and 1470 is 10.

GCF(1450,1470) = 10

We will now calculate the prime factors of 1450 and 1470, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1450 and 1470.

How to find the GCF of 1450 and 1470?

We will first find the prime factorization of 1450 and 1470. After we will calculate the factors of 1450 and 1470 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 1470

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

1470 = 2¹ × 3¹ × 5¹ × 7²

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 1470

List of positive integer factors of 1470 that divides 1450 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1450 and 1470. The biggest common factor number is the GCF number.
So the greatest common factor 1450 and 1470 is 10.

Also check out the Least Common Multiple of 1450 and 1470