What is the Greatest Common Factor of 1506 and 1523?

Greatest common factor (GCF) of 1506 and 1523 is 1.

GCF(1506,1523) = 1

We will now calculate the prime factors of 1506 and 1523, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1506 and 1523.

How to find the GCF of 1506 and 1523?

We will first find the prime factorization of 1506 and 1523. After we will calculate the factors of 1506 and 1523 and find the biggest common factor number .

Step-1: Prime Factorization of 1506

Prime factors of 1506 are 2, 3, 251. Prime factorization of 1506 in exponential form is:

1506 = 2¹ × 3¹ × 251¹

Step-2: Prime Factorization of 1523

Prime factors of 1523 are 1523. Prime factorization of 1523 in exponential form is:

1523 = 1523¹

Step-3: Factors of 1506

List of positive integer factors of 1506 that divides 1506 without a remainder.

1, 2, 3, 6, 251, 502, 753

Step-4: Factors of 1523

List of positive integer factors of 1523 that divides 1506 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1506 and 1523. The biggest common factor number is the GCF number.
So the greatest common factor 1506 and 1523 is 1.

Also check out the Least Common Multiple of 1506 and 1523