Greatest Common Factor of 546 and 553

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 546, 553 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 546 and 553 is 7.

GCF(546,553) = 7

GCF of 546 and 553

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

GCF of:
and

Greatest Common Factor of 546 and 553

GCF of 546 and 553 is 7

Prime Factorization of 546


2 546
3 273
7 91
13 13
1

Prime factors of 546 are 2,3,7,13. Prime factorization of 546 in exponential form is:

546 = 21×31×71×131

Prime Factorization of 553


7 553
79 79
1

Prime factors of 553 are 7,79. Prime factorization of 553 in exponential form is:

553 = 71×791

∴ So by taking common prime factors GCF of 546 and 553 is 7

Greatest Common Factor of 546 and 553 by matching factors method

Factors of 546

List of positive integer factors of 546 that divides 546 without a remainder.

1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546

Factors of 553

List of positive integer factors of 553 that divides 553 without a remainder.

1,7,79,553

Greatest Common Factor

We found the factors and prime factorization of 546 and 553. The biggest common factor number is the GCF number.
So the greatest common factor 546 and 553 is 7.

Also check out the Least Common Multiple of 546 and 553

Properties of GCF 546 and 553

(i) The GCF of 546 and 553 is associative

GCF of 546 and 553 = GCF of 553 and 546

Related Greatest Common Factor of 546

Related Greatest Common Factor of 553

Frequently Asked Questions on GCF of 546 and 553

1. What is the GCF of 546 and 553?

Answer: GCF of 546 and 553 is 7.

2. What are the Factors of 546?

Answer: Factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546. There are 16 integers that are factors of 546. The greatest factor of 546 is 546.

3. What are the Factors of 553?

Answer: Factors of 553 are 1, 7, 79, 553. There are 4 integers that are factors of 553. The greatest factor of 553 is 553.

4. How to Find the GCF of 546 and 553?

Answer:

Greatest Common Factor of 546 and 553 = 7

Step 1: Find the prime factorization of 546

546 = 2 x 3 x 7 x 13

Step 2: Find the prime factorization of 553

553 = 7 x 79

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

GCF = 7

Step 4: Therefore, the greatest common factor of 546 and 553 is 7