What is the Greatest Common Factor of 1542 and 1560?

Greatest common factor (GCF) of 1542 and 1560 is 6.

GCF(1542,1560) = 6

We will now calculate the prime factors of 1542 and 1560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1542 and 1560.

How to find the GCF of 1542 and 1560?

We will first find the prime factorization of 1542 and 1560. After we will calculate the factors of 1542 and 1560 and find the biggest common factor number .

Step-1: Prime Factorization of 1542

Prime factors of 1542 are 2, 3, 257. Prime factorization of 1542 in exponential form is:

1542 = 2¹ × 3¹ × 257¹

Step-2: 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-3: Factors of 1542

List of positive integer factors of 1542 that divides 1542 without a remainder.

1, 2, 3, 6, 257, 514, 771

Step-4: Factors of 1560

List of positive integer factors of 1560 that divides 1542 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1542 and 1560. The biggest common factor number is the GCF number.
So the greatest common factor 1542 and 1560 is 6.

Also check out the Least Common Multiple of 1542 and 1560