Greatest Common Factor of 1984 and 1991

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 1984, 1991 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1984 and 1991 is 1.

GCF(1984,1991) = 1

GCF of 1984 and 1991

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

GCF of:
and

Greatest Common Factor of 1984 and 1991

GCF of 1984 and 1991 is 1

Prime Factorization of 1984


2 1984
2 992
2 496
2 248
2 124
2 62
31 31
1

Prime factors of 1984 are 2,31. Prime factorization of 1984 in exponential form is:

1984 = 26×311

Prime Factorization of 1991


11 1991
181 181
1

Prime factors of 1991 are 11,181. Prime factorization of 1991 in exponential form is:

1991 = 111×1811

∴ So by taking common prime factors GCF of 1984 and 1991 is 1

Greatest Common Factor of 1984 and 1991 by matching factors method

Factors of 1984

List of positive integer factors of 1984 that divides 1984 without a remainder.

1,2,4,8,16,31,32,62,64,124,248,496,992,1984

Factors of 1991

List of positive integer factors of 1991 that divides 1991 without a remainder.

1,11,181,1991

Greatest Common Factor

We found the factors and prime factorization of 1984 and 1991. The biggest common factor number is the GCF number.
So the greatest common factor 1984 and 1991 is 1.

Also check out the Least Common Multiple of 1984 and 1991

Properties of GCF 1984 and 1991

(i) The GCF of 1984 and 1991 is associative

GCF of 1984 and 1991 = GCF of 1991 and 1984

Related Greatest Common Factor of 1984

Related Greatest Common Factor of 1991

Frequently Asked Questions on GCF of 1984 and 1991

1. What is the GCF of 1984 and 1991?

Answer: GCF of 1984 and 1991 is 1.

2. What are the Factors of 1984?

Answer: Factors of 1984 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984. There are 14 integers that are factors of 1984. The greatest factor of 1984 is 1984.

3. What are the Factors of 1991?

Answer: Factors of 1991 are 1, 11, 181, 1991. There are 4 integers that are factors of 1991. The greatest factor of 1991 is 1991.

4. How to Find the GCF of 1984 and 1991?

Answer:

Greatest Common Factor of 1984 and 1991 = 1

Step 1: Find the prime factorization of 1984

1984 = 2 x 2 x 2 x 2 x 2 x 2 x 31

Step 2: Find the prime factorization of 1991

1991 = 11 x 181

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 1984 and 1991 is 1