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 1978, 1986 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1978 and 1986 is 2.
GCF(1978,1986) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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
Prime Factorization of 1986
2 | 1986 |
3 | 993 |
331 | 331 |
1 |
Prime factors of 1986 are 2,3,331. Prime factorization of 1986 in exponential form is:
1986 = 21×31×3311
∴ So by taking common prime factors GCF of 1978 and 1986 is 2
Factors of 1978
List of positive integer factors of 1978 that divides 1978 without a remainder.
1,2,23,43,46,86,989,1978
Factors of 1986
List of positive integer factors of 1986 that divides 1986 without a remainder.
1,2,3,6,331,662,993,1986
Greatest Common Factor
We found the factors and prime factorization of 1978 and 1986. The biggest common factor number is the GCF number.
So the greatest common factor 1978 and 1986 is 2.
Also check out the Least Common Multiple of 1978 and 1986
(i) The GCF of 1978 and 1986 is associative
GCF of 1978 and 1986 = GCF of 1986 and 1978
1. What is the GCF of 1978 and 1986?
Answer: GCF of 1978 and 1986 is 2.
2. 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.
3. What are the Factors of 1986?
Answer: Factors of 1986 are 1, 2, 3, 6, 331, 662, 993, 1986. There are 8 integers that are factors of 1986. The greatest factor of 1986 is 1986.
4. How to Find the GCF of 1978 and 1986?
Answer:
Greatest Common Factor of 1978 and 1986 = 2
Step 1: Find the prime factorization of 1978
1978 = 2 x 23 x 43
Step 2: Find the prime factorization of 1986
1986 = 2 x 3 x 331
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 1978 and 1986 is 2