How to Find GCF of 978/10, 312/456?

GCF of 978/10, 312/456

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 978/10, 312/456 i.e 6/2280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 978/10, 312/456.

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 978/10,312/456?

Given fractions are 978/10,312/456

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 978/10,312/456, numerators are 978,312

Denominators are 10,456

The GCF of 978,312 is 6 .

LCM of 10,456 is 2280.

The greatest common factor of 978/10,312/456 = [GCF of 978,312]/[LCM of 10,456]= 6/2280

Therefore, the GCF of 978/10,312/456 is 6/2280.

Greatest Common Factor of 978,312

To find the highest common factor of 978,312, we have to find the factors of both numbers and list the highest common factor.

The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978

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

The HCF of 978,312 is 6.

Lets's calculate GCF of 978,312

Greatest Common Factor (GCF) of 978,312 By Common Division

2	978, 312
3	489, 156
	163, 52

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 978,312 By Matching Biggest Common Factor Method

Now, list down the factors of 978

1,2,3,6,163,326,489,978

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 978,312 . The biggest common factor number is the GCF number.
So the greatest common factor 978,312 is 6.

Lets's calculate LCM of 10,456

Lowest Common Multiple of 10,456 using Common Division

2	10, 456
	5, 228

∴ So the LCM of the given numbers is 2 x 5 x 228 = 2280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/2280

Therefore, the GCF of Fractions 978/10,312/456 is 6/2280

Least Common Multiple of 10,456 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 10,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(10,456) = 2

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

GCF(10,456) x common factors =2 x 1 = 2

LCM(10,456) = ( 10 × 456 ) / 2

LCM(10,456) = 4560 / 2

LCM(10,456) = 2280

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FAQs on GCF of Fractions of 978/10, 312/456

1. What is the HCF of 978,312?

The HCF of 978,312 is 6

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 978/10, 312/456?

Answer: GCF of Numerators as per given numbers 978/10, 312/456 is

GCF of Numerators i.e. for 978,312 is 6

LCM of denominators i.e. for 10,456 is 2280.

Thus, GCF of Fractions is 6/2280.Finally, GCF of Fractions for 978/10, 312/456 is 6/2280.