How to Find GCF of 9708/396, 8478/156?

GCF of 9708/396, 8478/156

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 9708/396, 8478/156 i.e 6/5148 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9708/396, 8478/156.

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 9708/396,8478/156?

Given fractions are 9708/396,8478/156

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 9708/396,8478/156, numerators are 9708,8478

Denominators are 396,156

The GCF of 9708,8478 is 6 .

LCM of 396,156 is 5148.

The greatest common factor of 9708/396,8478/156 = [GCF of 9708,8478]/[LCM of 396,156]= 6/5148

Therefore, the GCF of 9708/396,8478/156 is 6/5148.

Greatest Common Factor of 9708,8478

To find the highest common factor of 9708,8478, we have to find the factors of both numbers and list the highest common factor.

The factors of 9708 are 1, 2, 3, 4, 6, 12, 809, 1618, 2427, 3236, 4854, 9708

The factors of 8478 are 1, 2, 3, 6, 9, 18, 27, 54, 157, 314, 471, 942, 1413, 2826, 4239, 8478

The HCF of 9708,8478 is 6.

Lets's calculate GCF of 9708,8478

Greatest Common Factor (GCF) of 9708,8478 By Common Division

2	9708, 8478
3	4854, 4239
	1618, 1413

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

Greatest Common Factor of 9708,8478 By Matching Biggest Common Factor Method

Now, list down the factors of 9708

1,2,3,4,6,12,809,1618,2427,3236,4854,9708

Now, list down the factors of 8478

1,2,3,6,9,18,27,54,157,314,471,942,1413,2826,4239,8478

Greatest Common Factor

We found the factors 9708,8478 . The biggest common factor number is the GCF number.
So the greatest common factor 9708,8478 is 6.

Lets's calculate LCM of 396,156

Lowest Common Multiple of 396,156 using Common Division

2	396, 156
2	198, 78
3	99, 39
	33, 13

∴ So the LCM of the given numbers is 2 x 2 x 3 x 33 x 13 = 5148

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/5148

Therefore, the GCF of Fractions 9708/396,8478/156 is 6/5148

Least Common Multiple of 396,156 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 396,156 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(396,156) = 12

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

GCF(396,156) x common factors =12 x 1 = 12

LCM(396,156) = ( 396 × 156 ) / 12

LCM(396,156) = 61776 / 12

LCM(396,156) = 5148

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 9708/396, 8478/156

1. What is the HCF of 9708,8478?

The HCF of 9708,8478 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 9708/396, 8478/156?

Answer: GCF of Numerators as per given numbers 9708/396, 8478/156 is

GCF of Numerators i.e. for 9708,8478 is 6

LCM of denominators i.e. for 396,156 is 5148.

Thus, GCF of Fractions is 6/5148.Finally, GCF of Fractions for 9708/396, 8478/156 is 6/5148.