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 1960, 1967 i.e. 7 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1960 and 1967 is 7.
GCF(1960,1967) = 7
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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
Prime Factorization of 1967
7 | 1967 |
281 | 281 |
1 |
Prime factors of 1967 are 7,281. Prime factorization of 1967 in exponential form is:
1967 = 71×2811
∴ So by taking common prime factors GCF of 1960 and 1967 is 7
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
Factors of 1967
List of positive integer factors of 1967 that divides 1967 without a remainder.
1,7,281,1967
Greatest Common Factor
We found the factors and prime factorization of 1960 and 1967. The biggest common factor number is the GCF number.
So the greatest common factor 1960 and 1967 is 7.
Also check out the Least Common Multiple of 1960 and 1967
(i) The GCF of 1960 and 1967 is associative
GCF of 1960 and 1967 = GCF of 1967 and 1960
1. What is the GCF of 1960 and 1967?
Answer: GCF of 1960 and 1967 is 7.
2. 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.
3. What are the Factors of 1967?
Answer: Factors of 1967 are 1, 7, 281, 1967. There are 4 integers that are factors of 1967. The greatest factor of 1967 is 1967.
4. How to Find the GCF of 1960 and 1967?
Answer:
Greatest Common Factor of 1960 and 1967 = 7
Step 1: Find the prime factorization of 1960
1960 = 2 x 2 x 2 x 5 x 7 x 7
Step 2: Find the prime factorization of 1967
1967 = 7 x 281
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 1960 and 1967 is 7