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GCF of 721/768, 105/220

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 721/768, 105/220 i.e 7/42240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 721/768, 105/220.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 721/768,105/220?

Given fractions are 721/768,105/220

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 721/768,105/220, numerators are 721,105

Denominators are 768,220

The GCF of 721,105 is 7 .

LCM of 768,220 is 42240.

The greatest common factor of 721/768,105/220 = [GCF of 721,105]/[LCM of 768,220]= 7/42240

Therefore, the GCF of 721/768,105/220 is 7/42240.

Greatest Common Factor of 721,105

To find the highest common factor of 721,105, we have to find the factors of both numbers and list the highest common factor.

The factors of 721 are 1, 7, 103, 721

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

The HCF of 721,105 is 7.

Lets's calculate GCF of 721,105

Greatest Common Factor (GCF) of 721,105 By Common Division

7 721, 105
103, 15

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 721,105 By Matching Biggest Common Factor Method

Greatest Common Factor of 721,105 By Matching Biggest Common Factor Method

Now, list down the factors of 721

:

1,7,103,721

Now, list down the factors of 105

:

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors 721,105 . The biggest common factor number is the GCF number.
So the greatest common factor 721,105 is 7.

Lets's calculate LCM of 768,220

Lowest Common Multiple of 768,220 using Common Division

2 768, 220
2 384, 110
192, 55

∴ So the LCM of the given numbers is 2 x 2 x 192 x 55 = 42240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/42240

Therefore, the GCF of Fractions 721/768,105/220 is 7/42240

Least Common Multiple of 768,220 with GCF Formula

Least Common Multiple of 768,220 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 768,220 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(768,220) = 4

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

GCF(768,220) x common factors =4 x 1 = 4

LCM(768,220) = ( 768 × 220 ) / 4

LCM(768,220) = 168960 / 4

LCM(768,220) = 42240


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FAQs on GCF of Fractions of 721/768, 105/220

1. What is the HCF of 721,105?

The HCF of 721,105 is 7

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 721/768, 105/220?

Answer: GCF of Numerators as per given numbers 721/768, 105/220 is

GCF of Numerators i.e. for 721,105 is 7

LCM of denominators i.e. for 768,220 is 42240.

Thus, GCF of Fractions is 7/42240.Finally, GCF of Fractions for 721/768, 105/220 is 7/42240.