What is the Greatest Common Factor of 1530 and 1540?

Greatest common factor (GCF) of 1530 and 1540 is 10.

GCF(1530,1540) = 10

We will now calculate the prime factors of 1530 and 1540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1530 and 1540.

How to find the GCF of 1530 and 1540?

We will first find the prime factorization of 1530 and 1540. After we will calculate the factors of 1530 and 1540 and find the biggest common factor number .

Step-1: Prime Factorization of 1530

Prime factors of 1530 are 2, 3, 5, 17. Prime factorization of 1530 in exponential form is:

1530 = 2¹ × 3² × 5¹ × 17¹

Step-2: 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-3: Factors of 1530

List of positive integer factors of 1530 that divides 1530 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765

Step-4: Factors of 1540

List of positive integer factors of 1540 that divides 1530 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1530 and 1540. The biggest common factor number is the GCF number.
So the greatest common factor 1530 and 1540 is 10.

Also check out the Least Common Multiple of 1530 and 1540