How to Find GCF of 836/381, 416/431?

GCF of 836/381, 416/431

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 836/381, 416/431 i.e 4/164211 easily. The following is the detailed procedure to determine the greatest common factor of fractions 836/381, 416/431.

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 836/381,416/431?

Given fractions are 836/381,416/431

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 836/381,416/431, numerators are 836,416

Denominators are 381,431

The GCF of 836,416 is 4 .

LCM of 381,431 is 164211.

The greatest common factor of 836/381,416/431 = [GCF of 836,416]/[LCM of 381,431]= 4/164211

Therefore, the GCF of 836/381,416/431 is 4/164211.

Greatest Common Factor of 836,416

To find the highest common factor of 836,416, we have to find the factors of both numbers and list the highest common factor.

The factors of 836 are 1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836

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

The HCF of 836,416 is 4.

Lets's calculate GCF of 836,416

Greatest Common Factor (GCF) of 836,416 By Common Division

2	836, 416
2	418, 208
	209, 104

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 836,416 By Matching Biggest Common Factor Method

Now, list down the factors of 836

1,2,4,11,19,22,38,44,76,209,418,836

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 836,416 . The biggest common factor number is the GCF number.
So the greatest common factor 836,416 is 4.

Lets's calculate LCM of 381,431

Lowest Common Multiple of 381,431 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 164211

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/164211

Therefore, the GCF of Fractions 836/381,416/431 is 4/164211

Least Common Multiple of 381,431 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 381,431 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(381,431) = 1

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

GCF(381,431) x common factors =1 x 1 = 1

LCM(381,431) = ( 381 × 431 ) / 1

LCM(381,431) = 164211 / 1

LCM(381,431) = 164211

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FAQs on GCF of Fractions of 836/381, 416/431

1. What is the HCF of 836,416?

The HCF of 836,416 is 4

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 836/381, 416/431?

Answer: GCF of Numerators as per given numbers 836/381, 416/431 is

GCF of Numerators i.e. for 836,416 is 4

LCM of denominators i.e. for 381,431 is 164211.

Thus, GCF of Fractions is 4/164211.Finally, GCF of Fractions for 836/381, 416/431 is 4/164211.