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 1971, 1978 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1971 and 1978 is 1.
GCF(1971,1978) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 1971
3 | 1971 |
3 | 657 |
3 | 219 |
73 | 73 |
1 |
Prime factors of 1971 are 3,73. Prime factorization of 1971 in exponential form is:
1971 = 33×731
Prime Factorization of 1978
2 | 1978 |
23 | 989 |
43 | 43 |
1 |
Prime factors of 1978 are 2,23,43. Prime factorization of 1978 in exponential form is:
1978 = 21×231×431
∴ So by taking common prime factors GCF of 1971 and 1978 is 1
Factors of 1971
List of positive integer factors of 1971 that divides 1971 without a remainder.
1,3,9,27,73,219,657,1971
Factors of 1978
List of positive integer factors of 1978 that divides 1978 without a remainder.
1,2,23,43,46,86,989,1978
Greatest Common Factor
We found the factors and prime factorization of 1971 and 1978. The biggest common factor number is the GCF number.
So the greatest common factor 1971 and 1978 is 1.
Also check out the Least Common Multiple of 1971 and 1978
(i) The GCF of 1971 and 1978 is associative
GCF of 1971 and 1978 = GCF of 1978 and 1971
1. What is the GCF of 1971 and 1978?
Answer: GCF of 1971 and 1978 is 1.
2. What are the Factors of 1971?
Answer: Factors of 1971 are 1, 3, 9, 27, 73, 219, 657, 1971. There are 8 integers that are factors of 1971. The greatest factor of 1971 is 1971.
3. What are the Factors of 1978?
Answer: Factors of 1978 are 1, 2, 23, 43, 46, 86, 989, 1978. There are 8 integers that are factors of 1978. The greatest factor of 1978 is 1978.
4. How to Find the GCF of 1971 and 1978?
Answer:
Greatest Common Factor of 1971 and 1978 = 1
Step 1: Find the prime factorization of 1971
1971 = 3 x 3 x 3 x 73
Step 2: Find the prime factorization of 1978
1978 = 2 x 23 x 43
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = = 1
Step 4: Therefore, the greatest common factor of 1971 and 1978 is 1