What is the Greatest Common Factor of 1566 and 1586?

Greatest common factor (GCF) of 1566 and 1586 is 2.

GCF(1566,1586) = 2

We will now calculate the prime factors of 1566 and 1586, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1566 and 1586.

How to find the GCF of 1566 and 1586?

We will first find the prime factorization of 1566 and 1586. After we will calculate the factors of 1566 and 1586 and find the biggest common factor number .

Step-1: Prime Factorization of 1566

Prime factors of 1566 are 2, 3, 29. Prime factorization of 1566 in exponential form is:

1566 = 2¹ × 3³ × 29¹

Step-2: Prime Factorization of 1586

Prime factors of 1586 are 2, 13, 61. Prime factorization of 1586 in exponential form is:

1586 = 2¹ × 13¹ × 61¹

Step-3: Factors of 1566

List of positive integer factors of 1566 that divides 1566 without a remainder.

1, 2, 3, 6, 9, 18, 27, 29, 54, 58, 87, 174, 261, 522, 783

Step-4: Factors of 1586

List of positive integer factors of 1586 that divides 1566 without a remainder.

1, 2, 13, 26, 61, 122, 793

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1566 and 1586. The biggest common factor number is the GCF number.
So the greatest common factor 1566 and 1586 is 2.

Also check out the Least Common Multiple of 1566 and 1586