How to Find GCF of 123/49, 961/87, 107/64?

GCF of 123/49, 961/87, 107/64

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 123/49, 961/87, 107/64 i.e 1/272832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 123/49, 961/87, 107/64.

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 123/49,961/87,107/64?

Given fractions are 123/49,961/87,107/64

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 123/49,961/87,107/64, numerators are 123,961,107

Denominators are 49,87,64

The GCF of 123,961,107 is 1 .

LCM of 49,87,64 is 272832.

The greatest common factor of 123/49,961/87,107/64 = [GCF of 123,961,107]/[LCM of 49,87,64]= 1/272832

Therefore, the GCF of 123/49,961/87,107/64 is 1/272832.

Greatest Common Factor of 123,961,107

To find the highest common factor of 123,961,107, we have to find the factors of both numbers and list the highest common factor.

The factors of 123 are 1, 3, 41, 123

The factors of 961 are 1, 31, 961

The factors of 107 are 1, 107

The HCF of 123,961,107 is 1.

Lets's calculate GCF of 123,961,107

Greatest Common Factor (GCF) of 123,961,107 By Common Division

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

Greatest Common Factor of 123,961,107 By Matching Biggest Common Factor Method

Now, list down the factors of 123

1,3,41,123

Now, list down the factors of 961

1,31,961

Now, list down the factors of 107

1,107

Greatest Common Factor

We found the factors 123,961,107 . The biggest common factor number is the GCF number.
So the greatest common factor 123,961,107 is 1.

Lets's calculate LCM of 49,87,64

Lowest Common Multiple of 49,87,64 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 272832

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/272832

Therefore, the GCF of Fractions 123/49,961/87,107/64 is 1/272832

Least Common Multiple of 49,87,64 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 49,87,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(49,87,64) = 1

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

GCF(49,87,64) x common factors =1 x 1 = 1

LCM(49,87,64) = ( 49 × 87 × 64 ) / 1

LCM(49,87,64) = 272832 / 1

LCM(49,87,64) = 272832

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FAQs on GCF of Fractions of 123/49, 961/87, 107/64

1. What is the HCF of 123,961,107?

The HCF of 123,961,107 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 123/49, 961/87, 107/64?

Answer: GCF of Numerators as per given numbers 123/49, 961/87, 107/64 is

GCF of Numerators i.e. for 123,961,107 is 1

LCM of denominators i.e. for 49,87,64 is 272832.

Thus, GCF of Fractions is 1/272832.Finally, GCF of Fractions for 123/49, 961/87, 107/64 is 1/272832.