How to Find GCF of 996/59, 312/682?

GCF of 996/59, 312/682

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 996/59, 312/682 i.e 12/40238 easily. The following is the detailed procedure to determine the greatest common factor of fractions 996/59, 312/682.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 996/59,312/682?

Given fractions are 996/59,312/682

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 996/59,312/682, numerators are 996,312

Denominators are 59,682

The GCF of 996,312 is 12 .

LCM of 59,682 is 40238.

The greatest common factor of 996/59,312/682 = [GCF of 996,312]/[LCM of 59,682]= 12/40238

Therefore, the GCF of 996/59,312/682 is 12/40238.

Greatest Common Factor of 996,312

To find the highest common factor of 996,312, we have to find the factors of both numbers and list the highest common factor.

The factors of 996 are 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The HCF of 996,312 is 12.

Lets's calculate GCF of 996,312

Greatest Common Factor (GCF) of 996,312 By Common Division

2	996, 312
2	498, 156
3	249, 78
	83, 26

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 996,312 By Matching Biggest Common Factor Method

Now, list down the factors of 996

1,2,3,4,6,12,83,166,249,332,498,996

Now, list down the factors of 312

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 996,312 . The biggest common factor number is the GCF number.
So the greatest common factor 996,312 is 12.

Lets's calculate LCM of 59,682

Lowest Common Multiple of 59,682 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 40238

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/40238

Therefore, the GCF of Fractions 996/59,312/682 is 12/40238

Least Common Multiple of 59,682 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 59,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(59,682) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(59,682) x common factors =1 x 1 = 1

LCM(59,682) = ( 59 × 682 ) / 1

LCM(59,682) = 40238 / 1

LCM(59,682) = 40238

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FAQs on GCF of Fractions of 996/59, 312/682

1. What is the HCF of 996,312?

The HCF of 996,312 is 12

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 996/59, 312/682?

Answer: GCF of Numerators as per given numbers 996/59, 312/682 is

GCF of Numerators i.e. for 996,312 is 12

LCM of denominators i.e. for 59,682 is 40238.

Thus, GCF of Fractions is 12/40238.Finally, GCF of Fractions for 996/59, 312/682 is 12/40238.