Greatest Common Factor of 84 and 98

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 84, 98 i.e. 14 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 84 and 98 is 14.

GCF(84,98) = 14

GCF of 84 and 98

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

GCF of:
and

Greatest Common Factor of 84 and 98

GCF of 84 and 98 is 14

Prime Factorization of 84


2 84
2 42
3 21
7 7
1

Prime factors of 84 are 2,3,7. Prime factorization of 84 in exponential form is:

84 = 22×31×71

Prime Factorization of 98


2 98
7 49
7 7
1

Prime factors of 98 are 2,7. Prime factorization of 98 in exponential form is:

98 = 21×72

∴ So by taking common prime factors GCF of 84 and 98 is 14

Greatest Common Factor of 84 and 98 by matching factors method

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1,2,3,4,6,7,12,14,21,28,42,84

Factors of 98

List of positive integer factors of 98 that divides 98 without a remainder.

1,2,7,14,49,98

Greatest Common Factor

We found the factors and prime factorization of 84 and 98. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 98 is 14.

Also check out the Least Common Multiple of 84 and 98

Properties of GCF 84 and 98

(i) The GCF of 84 and 98 is associative

GCF of 84 and 98 = GCF of 98 and 84

Related Greatest Common Factor of 84

Related Greatest Common Factor of 98

Frequently Asked Questions on GCF of 84 and 98

1. What is the GCF of 84 and 98?

Answer: GCF of 84 and 98 is 14.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

3. What are the Factors of 98?

Answer: Factors of 98 are 1, 2, 7, 14, 49, 98. There are 6 integers that are factors of 98. The greatest factor of 98 is 98.

4. How to Find the GCF of 84 and 98?

Answer:

Greatest Common Factor of 84 and 98 = 14

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 98

98 = 2 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 x 7 = 14

Step 4: Therefore, the greatest common factor of 84 and 98 is 14