What is the Greatest Common Factor of 1540 and 1560?

Greatest common factor (GCF) of 1540 and 1560 is 20.

GCF(1540,1560) = 20

We will now calculate the prime factors of 1540 and 1560, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1540 and 1560.

How to find the GCF of 1540 and 1560?

We will first find the prime factorization of 1540 and 1560. After we will calculate the factors of 1540 and 1560 and find the biggest common factor number .

Step-1: Prime Factorization of 1540

Prime factors of 1540 are 2, 5, 7, 11. Prime factorization of 1540 in exponential form is:

1540 = 2² × 5¹ × 7¹ × 11¹

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 1540

List of positive integer factors of 1540 that divides 1540 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770

Step-4: Factors of 1560

List of positive integer factors of 1560 that divides 1540 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 1540 and 1560. The biggest common factor number is the GCF number.
So the greatest common factor 1540 and 1560 is 20.

Also check out the Least Common Multiple of 1540 and 1560