How to Find GCF of 3751/556, 4114/1040?

GCF of 3751/556, 4114/1040

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 3751/556, 4114/1040 i.e 121/144560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3751/556, 4114/1040.

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 3751/556,4114/1040?

Given fractions are 3751/556,4114/1040

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 3751/556,4114/1040, numerators are 3751,4114

Denominators are 556,1040

The GCF of 3751,4114 is 121 .

LCM of 556,1040 is 144560.

The greatest common factor of 3751/556,4114/1040 = [GCF of 3751,4114]/[LCM of 556,1040]= 121/144560

Therefore, the GCF of 3751/556,4114/1040 is 121/144560.

Greatest Common Factor of 3751,4114

To find the highest common factor of 3751,4114, we have to find the factors of both numbers and list the highest common factor.

The factors of 3751 are 1, 11, 31, 121, 341, 3751

The factors of 4114 are 1, 2, 11, 17, 22, 34, 121, 187, 242, 374, 2057, 4114

The HCF of 3751,4114 is 121.

Lets's calculate GCF of 3751,4114

Greatest Common Factor (GCF) of 3751,4114 By Common Division

11	3751, 4114
11	341, 374
	31, 34

∴ So the GCF of the given numbers is 11 x 11 = 121

Greatest Common Factor of 3751,4114 By Matching Biggest Common Factor Method

Now, list down the factors of 3751

1,11,31,121,341,3751

Now, list down the factors of 4114

1,2,11,17,22,34,121,187,242,374,2057,4114

Greatest Common Factor

We found the factors 3751,4114 . The biggest common factor number is the GCF number.
So the greatest common factor 3751,4114 is 121.

Lets's calculate LCM of 556,1040

Lowest Common Multiple of 556,1040 using Common Division

2	556, 1040
2	278, 520
	139, 260

∴ So the LCM of the given numbers is 2 x 2 x 139 x 260 = 144560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 121/144560

Therefore, the GCF of Fractions 3751/556,4114/1040 is 121/144560

Least Common Multiple of 556,1040 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 556,1040 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(556,1040) = 4

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

GCF(556,1040) x common factors =4 x 1 = 4

LCM(556,1040) = ( 556 × 1040 ) / 4

LCM(556,1040) = 578240 / 4

LCM(556,1040) = 144560

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FAQs on GCF of Fractions of 3751/556, 4114/1040

1. What is the HCF of 3751,4114?

The HCF of 3751,4114 is 121

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 3751/556, 4114/1040?

Answer: GCF of Numerators as per given numbers 3751/556, 4114/1040 is

GCF of Numerators i.e. for 3751,4114 is 121

LCM of denominators i.e. for 556,1040 is 144560.

Thus, GCF of Fractions is 121/144560.Finally, GCF of Fractions for 3751/556, 4114/1040 is 121/144560.