What is the Greatest Common Factor of 1568 and 1582?

Greatest common factor (GCF) of 1568 and 1582 is 14.

GCF(1568,1582) = 14

We will now calculate the prime factors of 1568 and 1582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1568 and 1582.

How to find the GCF of 1568 and 1582?

We will first find the prime factorization of 1568 and 1582. After we will calculate the factors of 1568 and 1582 and find the biggest common factor number .

Step-1: Prime Factorization of 1568

Prime factors of 1568 are 2, 7. Prime factorization of 1568 in exponential form is:

1568 = 2⁵ × 7²

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 1568

List of positive integer factors of 1568 that divides 1568 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784

Step-4: Factors of 1582

List of positive integer factors of 1582 that divides 1568 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1568 and 1582. The biggest common factor number is the GCF number.
So the greatest common factor 1568 and 1582 is 14.

Also check out the Least Common Multiple of 1568 and 1582