How to Find GCF of 914/688, 288/168?

GCF of 914/688, 288/168

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 914/688, 288/168 i.e 2/14448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 914/688, 288/168.

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 914/688,288/168?

Given fractions are 914/688,288/168

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 914/688,288/168, numerators are 914,288

Denominators are 688,168

The GCF of 914,288 is 2 .

LCM of 688,168 is 14448.

The greatest common factor of 914/688,288/168 = [GCF of 914,288]/[LCM of 688,168]= 2/14448

Therefore, the GCF of 914/688,288/168 is 2/14448.

Greatest Common Factor of 914,288

To find the highest common factor of 914,288, we have to find the factors of both numbers and list the highest common factor.

The factors of 914 are 1, 2, 457, 914

The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

The HCF of 914,288 is 2.

Lets's calculate GCF of 914,288

Greatest Common Factor (GCF) of 914,288 By Common Division

2	914, 288
	457, 144

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

Greatest Common Factor of 914,288 By Matching Biggest Common Factor Method

Now, list down the factors of 914

1,2,457,914

Now, list down the factors of 288

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Greatest Common Factor

We found the factors 914,288 . The biggest common factor number is the GCF number.
So the greatest common factor 914,288 is 2.

Lets's calculate LCM of 688,168

Lowest Common Multiple of 688,168 using Common Division

2	688, 168
2	344, 84
2	172, 42
	86, 21

∴ So the LCM of the given numbers is 2 x 2 x 2 x 86 x 21 = 14448

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14448

Therefore, the GCF of Fractions 914/688,288/168 is 2/14448

Least Common Multiple of 688,168 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 688,168 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(688,168) = 8

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

GCF(688,168) x common factors =8 x 1 = 8

LCM(688,168) = ( 688 × 168 ) / 8

LCM(688,168) = 115584 / 8

LCM(688,168) = 14448

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FAQs on GCF of Fractions of 914/688, 288/168

1. What is the HCF of 914,288?

The HCF of 914,288 is 2

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 914/688, 288/168?

Answer: GCF of Numerators as per given numbers 914/688, 288/168 is

GCF of Numerators i.e. for 914,288 is 2

LCM of denominators i.e. for 688,168 is 14448.

Thus, GCF of Fractions is 2/14448.Finally, GCF of Fractions for 914/688, 288/168 is 2/14448.