How to Find GCF of 832/278, 6348/409?

GCF of 832/278, 6348/409

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 832/278, 6348/409 i.e 4/113702 easily. The following is the detailed procedure to determine the greatest common factor of fractions 832/278, 6348/409.

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 832/278,6348/409?

Given fractions are 832/278,6348/409

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 832/278,6348/409, numerators are 832,6348

Denominators are 278,409

The GCF of 832,6348 is 4 .

LCM of 278,409 is 113702.

The greatest common factor of 832/278,6348/409 = [GCF of 832,6348]/[LCM of 278,409]= 4/113702

Therefore, the GCF of 832/278,6348/409 is 4/113702.

Greatest Common Factor of 832,6348

To find the highest common factor of 832,6348, we have to find the factors of both numbers and list the highest common factor.

The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832

The factors of 6348 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276, 529, 1058, 1587, 2116, 3174, 6348

The HCF of 832,6348 is 4.

Lets's calculate GCF of 832,6348

Greatest Common Factor (GCF) of 832,6348 By Common Division

2	832, 6348
2	416, 3174
	208, 1587

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

Greatest Common Factor of 832,6348 By Matching Biggest Common Factor Method

Now, list down the factors of 832

1,2,4,8,13,16,26,32,52,64,104,208,416,832

Now, list down the factors of 6348

1,2,3,4,6,12,23,46,69,92,138,276,529,1058,1587,2116,3174,6348

Greatest Common Factor

We found the factors 832,6348 . The biggest common factor number is the GCF number.
So the greatest common factor 832,6348 is 4.

Lets's calculate LCM of 278,409

Lowest Common Multiple of 278,409 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 113702

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/113702

Therefore, the GCF of Fractions 832/278,6348/409 is 4/113702

Least Common Multiple of 278,409 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 278,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(278,409) = 1

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

GCF(278,409) x common factors =1 x 1 = 1

LCM(278,409) = ( 278 × 409 ) / 1

LCM(278,409) = 113702 / 1

LCM(278,409) = 113702

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FAQs on GCF of Fractions of 832/278, 6348/409

1. What is the HCF of 832,6348?

The HCF of 832,6348 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 832/278, 6348/409?

Answer: GCF of Numerators as per given numbers 832/278, 6348/409 is

GCF of Numerators i.e. for 832,6348 is 4

LCM of denominators i.e. for 278,409 is 113702.

Thus, GCF of Fractions is 4/113702.Finally, GCF of Fractions for 832/278, 6348/409 is 4/113702.