Greatest Common Factor of 1536 and 1542

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 1536, 1542 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1536 and 1542 is 6.

GCF(1536,1542) = 6

GCF of 1536 and 1542

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

GCF of:
and

Greatest Common Factor of 1536 and 1542

GCF of 1536 and 1542 is 6

Prime Factorization of 1536


2 1536
2 768
2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 1536 are 2,3. Prime factorization of 1536 in exponential form is:

1536 = 29×31

Prime Factorization of 1542


2 1542
3 771
257 257
1

Prime factors of 1542 are 2,3,257. Prime factorization of 1542 in exponential form is:

1542 = 21×31×2571

∴ So by taking common prime factors GCF of 1536 and 1542 is 6

Greatest Common Factor of 1536 and 1542 by matching factors method

Factors of 1536

List of positive integer factors of 1536 that divides 1536 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,512,768,1536

Factors of 1542

List of positive integer factors of 1542 that divides 1542 without a remainder.

1,2,3,6,257,514,771,1542

Greatest Common Factor

We found the factors and prime factorization of 1536 and 1542. The biggest common factor number is the GCF number.
So the greatest common factor 1536 and 1542 is 6.

Also check out the Least Common Multiple of 1536 and 1542

Properties of GCF 1536 and 1542

(i) The GCF of 1536 and 1542 is associative

GCF of 1536 and 1542 = GCF of 1542 and 1536

Related Greatest Common Factor of 1536

Related Greatest Common Factor of 1542

Frequently Asked Questions on GCF of 1536 and 1542

1. What is the GCF of 1536 and 1542?

Answer: GCF of 1536 and 1542 is 6.

2. What are the Factors of 1536?

Answer: Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536. There are 20 integers that are factors of 1536. The greatest factor of 1536 is 1536.

3. What are the Factors of 1542?

Answer: Factors of 1542 are 1, 2, 3, 6, 257, 514, 771, 1542. There are 8 integers that are factors of 1542. The greatest factor of 1542 is 1542.

4. How to Find the GCF of 1536 and 1542?

Answer:

Greatest Common Factor of 1536 and 1542 = 6

Step 1: Find the prime factorization of 1536

1536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 1542

1542 = 2 x 3 x 257

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 1536 and 1542 is 6