Greatest Common Factor of 1946 and 1953

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 1946, 1953 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1946 and 1953 is 7.

GCF(1946,1953) = 7

GCF of 1946 and 1953

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

GCF of:
and

Greatest Common Factor of 1946 and 1953

GCF of 1946 and 1953 is 7

Prime Factorization of 1946


2 1946
7 973
139 139
1

Prime factors of 1946 are 2,7,139. Prime factorization of 1946 in exponential form is:

1946 = 21×71×1391

Prime Factorization of 1953


3 1953
3 651
7 217
31 31
1

Prime factors of 1953 are 3,7,31. Prime factorization of 1953 in exponential form is:

1953 = 32×71×311

∴ So by taking common prime factors GCF of 1946 and 1953 is 7

Greatest Common Factor of 1946 and 1953 by matching factors method

Factors of 1946

List of positive integer factors of 1946 that divides 1946 without a remainder.

1,2,7,14,139,278,973,1946

Factors of 1953

List of positive integer factors of 1953 that divides 1953 without a remainder.

1,3,7,9,21,31,63,93,217,279,651,1953

Greatest Common Factor

We found the factors and prime factorization of 1946 and 1953. The biggest common factor number is the GCF number.
So the greatest common factor 1946 and 1953 is 7.

Also check out the Least Common Multiple of 1946 and 1953

Properties of GCF 1946 and 1953

(i) The GCF of 1946 and 1953 is associative

GCF of 1946 and 1953 = GCF of 1953 and 1946

Related Greatest Common Factor of 1946

Related Greatest Common Factor of 1953

Frequently Asked Questions on GCF of 1946 and 1953

1. What is the GCF of 1946 and 1953?

Answer: GCF of 1946 and 1953 is 7.

2. What are the Factors of 1946?

Answer: Factors of 1946 are 1, 2, 7, 14, 139, 278, 973, 1946. There are 8 integers that are factors of 1946. The greatest factor of 1946 is 1946.

3. What are the Factors of 1953?

Answer: Factors of 1953 are 1, 3, 7, 9, 21, 31, 63, 93, 217, 279, 651, 1953. There are 12 integers that are factors of 1953. The greatest factor of 1953 is 1953.

4. How to Find the GCF of 1946 and 1953?

Answer:

Greatest Common Factor of 1946 and 1953 = 7

Step 1: Find the prime factorization of 1946

1946 = 2 x 7 x 139

Step 2: Find the prime factorization of 1953

1953 = 3 x 3 x 7 x 31

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 1946 and 1953 is 7