What is the Greatest Common Factor of 1582 and 1596?

Greatest common factor (GCF) of 1582 and 1596 is 14.

GCF(1582,1596) = 14

We will now calculate the prime factors of 1582 and 1596, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1582 and 1596.

How to find the GCF of 1582 and 1596?

We will first find the prime factorization of 1582 and 1596. After we will calculate the factors of 1582 and 1596 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1596

Prime factors of 1596 are 2, 3, 7, 19. Prime factorization of 1596 in exponential form is:

1596 = 2² × 3¹ × 7¹ × 19¹

Step-3: Factors of 1582

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

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

Step-4: Factors of 1596

List of positive integer factors of 1596 that divides 1582 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 19, 21, 28, 38, 42, 57, 76, 84, 114, 133, 228, 266, 399, 532, 798

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1582 and 1596. The biggest common factor number is the GCF number.
So the greatest common factor 1582 and 1596 is 14.

Also check out the Least Common Multiple of 1582 and 1596