Greatest Common Factor of 1954 and 1960

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 1954, 1960 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1954 and 1960 is 2.

GCF(1954,1960) = 2

GCF of 1954 and 1960

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

GCF of:
and

Greatest Common Factor of 1954 and 1960

GCF of 1954 and 1960 is 2

Prime Factorization of 1954


2 1954
977 977
1

Prime factors of 1954 are 2,977. Prime factorization of 1954 in exponential form is:

1954 = 21×9771

Prime Factorization of 1960


2 1960
2 980
2 490
5 245
7 49
7 7
1

Prime factors of 1960 are 2,5,7. Prime factorization of 1960 in exponential form is:

1960 = 23×51×72

∴ So by taking common prime factors GCF of 1954 and 1960 is 2

Greatest Common Factor of 1954 and 1960 by matching factors method

Factors of 1954

List of positive integer factors of 1954 that divides 1954 without a remainder.

1,2,977,1954

Factors of 1960

List of positive integer factors of 1960 that divides 1960 without a remainder.

1,2,4,5,7,8,10,14,20,28,35,40,49,56,70,98,140,196,245,280,392,490,980,1960

Greatest Common Factor

We found the factors and prime factorization of 1954 and 1960. The biggest common factor number is the GCF number.
So the greatest common factor 1954 and 1960 is 2.

Also check out the Least Common Multiple of 1954 and 1960

Properties of GCF 1954 and 1960

(i) The GCF of 1954 and 1960 is associative

GCF of 1954 and 1960 = GCF of 1960 and 1954

Related Greatest Common Factor of 1954

Related Greatest Common Factor of 1960

Frequently Asked Questions on GCF of 1954 and 1960

1. What is the GCF of 1954 and 1960?

Answer: GCF of 1954 and 1960 is 2.

2. What are the Factors of 1954?

Answer: Factors of 1954 are 1, 2, 977, 1954. There are 4 integers that are factors of 1954. The greatest factor of 1954 is 1954.

3. What are the Factors of 1960?

Answer: Factors of 1960 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960. There are 24 integers that are factors of 1960. The greatest factor of 1960 is 1960.

4. How to Find the GCF of 1954 and 1960?

Answer:

Greatest Common Factor of 1954 and 1960 = 2

Step 1: Find the prime factorization of 1954

1954 = 2 x 977

Step 2: Find the prime factorization of 1960

1960 = 2 x 2 x 2 x 5 x 7 x 7

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 1954 and 1960 is 2