Greatest Common Factor of 1506 and 1514

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1506, 1514 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1506 and 1514 is 2.

GCF(1506,1514) = 2

GCF of 1506 and 1514

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 1506 and 1514

GCF of 1506 and 1514 is 2

Prime Factorization of 1506


2 1506
3 753
251 251
1

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

1506 = 21×31×2511

Prime Factorization of 1514


2 1514
757 757
1

Prime factors of 1514 are 2,757. Prime factorization of 1514 in exponential form is:

1514 = 21×7571

∴ So by taking common prime factors GCF of 1506 and 1514 is 2

Greatest Common Factor of 1506 and 1514 by matching factors method

Factors of 1506

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

1,2,3,6,251,502,753,1506

Factors of 1514

List of positive integer factors of 1514 that divides 1514 without a remainder.

1,2,757,1514

Greatest Common Factor

We found the factors and prime factorization of 1506 and 1514. The biggest common factor number is the GCF number.
So the greatest common factor 1506 and 1514 is 2.

Also check out the Least Common Multiple of 1506 and 1514

Properties of GCF 1506 and 1514

(i) The GCF of 1506 and 1514 is associative

GCF of 1506 and 1514 = GCF of 1514 and 1506

Related Greatest Common Factor of 1506

Related Greatest Common Factor of 1514

Frequently Asked Questions on GCF of 1506 and 1514

1. What is the GCF of 1506 and 1514?

Answer: GCF of 1506 and 1514 is 2.

2. What are the Factors of 1506?

Answer: Factors of 1506 are 1, 2, 3, 6, 251, 502, 753, 1506. There are 8 integers that are factors of 1506. The greatest factor of 1506 is 1506.

3. What are the Factors of 1514?

Answer: Factors of 1514 are 1, 2, 757, 1514. There are 4 integers that are factors of 1514. The greatest factor of 1514 is 1514.

4. How to Find the GCF of 1506 and 1514?

Answer:

Greatest Common Factor of 1506 and 1514 = 2

Step 1: Find the prime factorization of 1506

1506 = 2 x 3 x 251

Step 2: Find the prime factorization of 1514

1514 = 2 x 757

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2

Step 4: Therefore, the greatest common factor of 1506 and 1514 is 2