How to Find GCF of 826/64, 960/678?

GCF of 826/64, 960/678

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 826/64, 960/678 i.e 2/21696 easily. The following is the detailed procedure to determine the greatest common factor of fractions 826/64, 960/678.

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 826/64,960/678?

Given fractions are 826/64,960/678

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 826/64,960/678, numerators are 826,960

Denominators are 64,678

The GCF of 826,960 is 2 .

LCM of 64,678 is 21696.

The greatest common factor of 826/64,960/678 = [GCF of 826,960]/[LCM of 64,678]= 2/21696

Therefore, the GCF of 826/64,960/678 is 2/21696.

Greatest Common Factor of 826,960

To find the highest common factor of 826,960, we have to find the factors of both numbers and list the highest common factor.

The factors of 826 are 1, 2, 7, 14, 59, 118, 413, 826

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960

The HCF of 826,960 is 2.

Lets's calculate GCF of 826,960

Greatest Common Factor (GCF) of 826,960 By Common Division

2	826, 960
	413, 480

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

Greatest Common Factor of 826,960 By Matching Biggest Common Factor Method

Now, list down the factors of 826

1,2,7,14,59,118,413,826

Now, list down the factors of 960

1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960

Greatest Common Factor

We found the factors 826,960 . The biggest common factor number is the GCF number.
So the greatest common factor 826,960 is 2.

Lets's calculate LCM of 64,678

Lowest Common Multiple of 64,678 using Common Division

2	64, 678
	32, 339

∴ So the LCM of the given numbers is 2 x 32 x 339 = 21696

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21696

Therefore, the GCF of Fractions 826/64,960/678 is 2/21696

Least Common Multiple of 64,678 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 64,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,678) = 2

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

GCF(64,678) x common factors =2 x 1 = 2

LCM(64,678) = ( 64 × 678 ) / 2

LCM(64,678) = 43392 / 2

LCM(64,678) = 21696

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FAQs on GCF of Fractions of 826/64, 960/678

1. What is the HCF of 826,960?

The HCF of 826,960 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 826/64, 960/678?

Answer: GCF of Numerators as per given numbers 826/64, 960/678 is

GCF of Numerators i.e. for 826,960 is 2

LCM of denominators i.e. for 64,678 is 21696.

Thus, GCF of Fractions is 2/21696.Finally, GCF of Fractions for 826/64, 960/678 is 2/21696.