How to Find GCF of 168/28, 632/8078?

GCF of 168/28, 632/8078

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 168/28, 632/8078 i.e 8/16156 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/28, 632/8078.

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 168/28,632/8078?

Given fractions are 168/28,632/8078

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 168/28,632/8078, numerators are 168,632

Denominators are 28,8078

The GCF of 168,632 is 8 .

LCM of 28,8078 is 16156.

The greatest common factor of 168/28,632/8078 = [GCF of 168,632]/[LCM of 28,8078]= 8/16156

Therefore, the GCF of 168/28,632/8078 is 8/16156.

Greatest Common Factor of 168,632

To find the highest common factor of 168,632, we have to find the factors of both numbers and list the highest common factor.

The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

The factors of 632 are 1, 2, 4, 8, 79, 158, 316, 632

The HCF of 168,632 is 8.

Lets's calculate GCF of 168,632

Greatest Common Factor (GCF) of 168,632 By Common Division

2	168, 632
2	84, 316
2	42, 158
	21, 79

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 168,632 By Matching Biggest Common Factor Method

Now, list down the factors of 168

1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168

Now, list down the factors of 632

1,2,4,8,79,158,316,632

Greatest Common Factor

We found the factors 168,632 . The biggest common factor number is the GCF number.
So the greatest common factor 168,632 is 8.

Lets's calculate LCM of 28,8078

Lowest Common Multiple of 28,8078 using Common Division

2	28, 8078
7	14, 4039
	2, 577

∴ So the LCM of the given numbers is 2 x 7 x 2 x 577 = 16156

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/16156

Therefore, the GCF of Fractions 168/28,632/8078 is 8/16156

Least Common Multiple of 28,8078 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 28,8078 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(28,8078) = 14

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

GCF(28,8078) x common factors =14 x 1 = 14

LCM(28,8078) = ( 28 × 8078 ) / 14

LCM(28,8078) = 226184 / 14

LCM(28,8078) = 16156

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FAQs on GCF of Fractions of 168/28, 632/8078

1. What is the HCF of 168,632?

The HCF of 168,632 is 8

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 168/28, 632/8078?

Answer: GCF of Numerators as per given numbers 168/28, 632/8078 is

GCF of Numerators i.e. for 168,632 is 8

LCM of denominators i.e. for 28,8078 is 16156.

Thus, GCF of Fractions is 8/16156.Finally, GCF of Fractions for 168/28, 632/8078 is 8/16156.