How to Find GCF of 7667/542, 4257/700?

GCF of 7667/542, 4257/700

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 7667/542, 4257/700 i.e 11/189700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7667/542, 4257/700.

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 7667/542,4257/700?

Given fractions are 7667/542,4257/700

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 7667/542,4257/700, numerators are 7667,4257

Denominators are 542,700

The GCF of 7667,4257 is 11 .

LCM of 542,700 is 189700.

The greatest common factor of 7667/542,4257/700 = [GCF of 7667,4257]/[LCM of 542,700]= 11/189700

Therefore, the GCF of 7667/542,4257/700 is 11/189700.

Greatest Common Factor of 7667,4257

To find the highest common factor of 7667,4257, we have to find the factors of both numbers and list the highest common factor.

The factors of 7667 are 1, 11, 17, 41, 187, 451, 697, 7667

The factors of 4257 are 1, 3, 9, 11, 33, 43, 99, 129, 387, 473, 1419, 4257

The HCF of 7667,4257 is 11.

Lets's calculate GCF of 7667,4257

Greatest Common Factor (GCF) of 7667,4257 By Common Division

11	7667, 4257
	697, 387

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

Greatest Common Factor of 7667,4257 By Matching Biggest Common Factor Method

Now, list down the factors of 7667

1,11,17,41,187,451,697,7667

Now, list down the factors of 4257

1,3,9,11,33,43,99,129,387,473,1419,4257

Greatest Common Factor

We found the factors 7667,4257 . The biggest common factor number is the GCF number.
So the greatest common factor 7667,4257 is 11.

Lets's calculate LCM of 542,700

Lowest Common Multiple of 542,700 using Common Division

2	542, 700
	271, 350

∴ So the LCM of the given numbers is 2 x 271 x 350 = 189700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/189700

Therefore, the GCF of Fractions 7667/542,4257/700 is 11/189700

Least Common Multiple of 542,700 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 542,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(542,700) = 2

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

GCF(542,700) x common factors =2 x 1 = 2

LCM(542,700) = ( 542 × 700 ) / 2

LCM(542,700) = 379400 / 2

LCM(542,700) = 189700

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FAQs on GCF of Fractions of 7667/542, 4257/700

1. What is the HCF of 7667,4257?

The HCF of 7667,4257 is 11

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 7667/542, 4257/700?

Answer: GCF of Numerators as per given numbers 7667/542, 4257/700 is

GCF of Numerators i.e. for 7667,4257 is 11

LCM of denominators i.e. for 542,700 is 189700.

Thus, GCF of Fractions is 11/189700.Finally, GCF of Fractions for 7667/542, 4257/700 is 11/189700.