What is the Greatest Common Factor of 1564 and 1582?

Greatest common factor (GCF) of 1564 and 1582 is 2.

GCF(1564,1582) = 2

We will now calculate the prime factors of 1564 and 1582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1564 and 1582.

How to find the GCF of 1564 and 1582?

We will first find the prime factorization of 1564 and 1582. After we will calculate the factors of 1564 and 1582 and find the biggest common factor number .

Step-1: Prime Factorization of 1564

Prime factors of 1564 are 2, 17, 23. Prime factorization of 1564 in exponential form is:

1564 = 2² × 17¹ × 23¹

Step-2: Prime Factorization of 1582

Prime factors of 1582 are 2, 7, 113. Prime factorization of 1582 in exponential form is:

1582 = 2¹ × 7¹ × 113¹

Step-3: Factors of 1564

List of positive integer factors of 1564 that divides 1564 without a remainder.

1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782

Step-4: Factors of 1582

List of positive integer factors of 1582 that divides 1564 without a remainder.

1, 2, 7, 14, 113, 226, 791

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1564 and 1582. The biggest common factor number is the GCF number.
So the greatest common factor 1564 and 1582 is 2.

Also check out the Least Common Multiple of 1564 and 1582