What is the Greatest Common Factor of 1560 and 1578?

Greatest common factor (GCF) of 1560 and 1578 is 6.

GCF(1560,1578) = 6

We will now calculate the prime factors of 1560 and 1578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1560 and 1578.

How to find the GCF of 1560 and 1578?

We will first find the prime factorization of 1560 and 1578. After we will calculate the factors of 1560 and 1578 and find the biggest common factor number .

Step-1: Prime Factorization of 1560

Prime factors of 1560 are 2, 3, 5, 13. Prime factorization of 1560 in exponential form is:

1560 = 2³ × 3¹ × 5¹ × 13¹

Step-2: Prime Factorization of 1578

Prime factors of 1578 are 2, 3, 263. Prime factorization of 1578 in exponential form is:

1578 = 2¹ × 3¹ × 263¹

Step-3: Factors of 1560

List of positive integer factors of 1560 that divides 1560 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780

Step-4: Factors of 1578

List of positive integer factors of 1578 that divides 1560 without a remainder.

1, 2, 3, 6, 263, 526, 789

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1560 and 1578. The biggest common factor number is the GCF number.
So the greatest common factor 1560 and 1578 is 6.

Also check out the Least Common Multiple of 1560 and 1578