How to Find GCF of 70/638, 57/814, 107/130?

GCF of 70/638, 57/814, 107/130

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 70/638, 57/814, 107/130 i.e 1/1534390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/638, 57/814, 107/130.

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 70/638,57/814,107/130?

Given fractions are 70/638,57/814,107/130

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 70/638,57/814,107/130, numerators are 70,57,107

Denominators are 638,814,130

The GCF of 70,57,107 is 1 .

LCM of 638,814,130 is 1534390.

The greatest common factor of 70/638,57/814,107/130 = [GCF of 70,57,107]/[LCM of 638,814,130]= 1/1534390

Therefore, the GCF of 70/638,57/814,107/130 is 1/1534390.

Greatest Common Factor of 70,57,107

To find the highest common factor of 70,57,107, we have to find the factors of both numbers and list the highest common factor.

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70

The factors of 57 are 1, 3, 19, 57

The factors of 107 are 1, 107

The HCF of 70,57,107 is 1.

Lets's calculate GCF of 70,57,107

Greatest Common Factor (GCF) of 70,57,107 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 70,57,107 By Matching Biggest Common Factor Method

Now, list down the factors of 70

1,2,5,7,10,14,35,70

Now, list down the factors of 57

1,3,19,57

Now, list down the factors of 107

1,107

Greatest Common Factor

We found the factors 70,57,107 . The biggest common factor number is the GCF number.
So the greatest common factor 70,57,107 is 1.

Lets's calculate LCM of 638,814,130

Lowest Common Multiple of 638,814,130 using Common Division

2	638, 814, 130
11	319, 407, 65
	29, 37, 65

∴ So the LCM of the given numbers is 2 x 11 x 29 x 37 x 65 = 1534390

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1534390

Therefore, the GCF of Fractions 70/638,57/814,107/130 is 1/1534390

Least Common Multiple of 638,814,130 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 638,814,130 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(638,814,130) = 2

common factors(in case of two or more numbers have common factors) = 22

GCF(638,814,130) x common factors =2 x 22 = 44

LCM(638,814,130) = ( 638 × 814 × 130 ) / 44

LCM(638,814,130) = 67513160 / 44

LCM(638,814,130) = 1534390

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 70/638, 57/814, 107/130

1. What is the HCF of 70,57,107?

The HCF of 70,57,107 is 1

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 70/638, 57/814, 107/130?

Answer: GCF of Numerators as per given numbers 70/638, 57/814, 107/130 is

GCF of Numerators i.e. for 70,57,107 is 1

LCM of denominators i.e. for 638,814,130 is 1534390.

Thus, GCF of Fractions is 1/1534390.Finally, GCF of Fractions for 70/638, 57/814, 107/130 is 1/1534390.