What is the Greatest Common Factor of 1590 and 1610?

Greatest common factor (GCF) of 1590 and 1610 is 10.

GCF(1590,1610) = 10

We will now calculate the prime factors of 1590 and 1610, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1590 and 1610.

How to find the GCF of 1590 and 1610?

We will first find the prime factorization of 1590 and 1610. After we will calculate the factors of 1590 and 1610 and find the biggest common factor number .

Step-1: Prime Factorization of 1590

Prime factors of 1590 are 2, 3, 5, 53. Prime factorization of 1590 in exponential form is:

1590 = 2¹ × 3¹ × 5¹ × 53¹

Step-2: Prime Factorization of 1610

Prime factors of 1610 are 2, 5, 7, 23. Prime factorization of 1610 in exponential form is:

1610 = 2¹ × 5¹ × 7¹ × 23¹

Step-3: Factors of 1590

List of positive integer factors of 1590 that divides 1590 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 53, 106, 159, 265, 318, 530, 795

Step-4: Factors of 1610

List of positive integer factors of 1610 that divides 1590 without a remainder.

1, 2, 5, 7, 10, 14, 23, 35, 46, 70, 115, 161, 230, 322, 805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1590 and 1610. The biggest common factor number is the GCF number.
So the greatest common factor 1590 and 1610 is 10.

Also check out the Least Common Multiple of 1590 and 1610