How to Find GCF of 256/42, 416/979?

GCF of 256/42, 416/979

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 256/42, 416/979 i.e 32/41118 easily. The following is the detailed procedure to determine the greatest common factor of fractions 256/42, 416/979.

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 256/42,416/979?

Given fractions are 256/42,416/979

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 256/42,416/979, numerators are 256,416

Denominators are 42,979

The GCF of 256,416 is 32 .

LCM of 42,979 is 41118.

The greatest common factor of 256/42,416/979 = [GCF of 256,416]/[LCM of 42,979]= 32/41118

Therefore, the GCF of 256/42,416/979 is 32/41118.

Greatest Common Factor of 256,416

To find the highest common factor of 256,416, we have to find the factors of both numbers and list the highest common factor.

The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

The HCF of 256,416 is 32.

Lets's calculate GCF of 256,416

Greatest Common Factor (GCF) of 256,416 By Common Division

2	256, 416
2	128, 208
2	64, 104
2	32, 52
2	16, 26
	8, 13

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 256,416 By Matching Biggest Common Factor Method

Now, list down the factors of 256

1,2,4,8,16,32,64,128,256

Now, list down the factors of 416

1,2,4,8,13,16,26,32,52,104,208,416

Greatest Common Factor

We found the factors 256,416 . The biggest common factor number is the GCF number.
So the greatest common factor 256,416 is 32.

Lets's calculate LCM of 42,979

Lowest Common Multiple of 42,979 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 41118

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/41118

Therefore, the GCF of Fractions 256/42,416/979 is 32/41118

Least Common Multiple of 42,979 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 42,979 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,979) = 1

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

GCF(42,979) x common factors =1 x 1 = 1

LCM(42,979) = ( 42 × 979 ) / 1

LCM(42,979) = 41118 / 1

LCM(42,979) = 41118

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FAQs on GCF of Fractions of 256/42, 416/979

1. What is the HCF of 256,416?

The HCF of 256,416 is 32

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 256/42, 416/979?

Answer: GCF of Numerators as per given numbers 256/42, 416/979 is

GCF of Numerators i.e. for 256,416 is 32

LCM of denominators i.e. for 42,979 is 41118.

Thus, GCF of Fractions is 32/41118.Finally, GCF of Fractions for 256/42, 416/979 is 32/41118.