What is the Greatest Common Factor of 1560 and 1565?

Greatest common factor (GCF) of 1560 and 1565 is 5.

GCF(1560,1565) = 5

We will now calculate the prime factors of 1560 and 1565, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1560 and 1565.

How to find the GCF of 1560 and 1565?

We will first find the prime factorization of 1560 and 1565. After we will calculate the factors of 1560 and 1565 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 1565

Prime factors of 1565 are 5, 313. Prime factorization of 1565 in exponential form is:

1565 = 5¹ × 313¹

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 1565

List of positive integer factors of 1565 that divides 1560 without a remainder.

1, 5, 313

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1560 and 1565. The biggest common factor number is the GCF number.
So the greatest common factor 1560 and 1565 is 5.

Also check out the Least Common Multiple of 1560 and 1565