How to Find GCF of 7757/416, 8386/900?

GCF of 7757/416, 8386/900

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 7757/416, 8386/900 i.e 1/93600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7757/416, 8386/900.

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 7757/416,8386/900?

Given fractions are 7757/416,8386/900

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 7757/416,8386/900, numerators are 7757,8386

Denominators are 416,900

The GCF of 7757,8386 is 1 .

LCM of 416,900 is 93600.

The greatest common factor of 7757/416,8386/900 = [GCF of 7757,8386]/[LCM of 416,900]= 1/93600

Therefore, the GCF of 7757/416,8386/900 is 1/93600.

Greatest Common Factor of 7757,8386

To find the highest common factor of 7757,8386, we have to find the factors of both numbers and list the highest common factor.

The factors of 7757 are 1, 7757

The factors of 8386 are 1, 2, 7, 14, 599, 1198, 4193, 8386

The HCF of 7757,8386 is 1.

Lets's calculate GCF of 7757,8386

Greatest Common Factor (GCF) of 7757,8386 By Common Division

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

Greatest Common Factor of 7757,8386 By Matching Biggest Common Factor Method

Now, list down the factors of 7757

1,7757

Now, list down the factors of 8386

1,2,7,14,599,1198,4193,8386

Greatest Common Factor

We found the factors 7757,8386 . The biggest common factor number is the GCF number.
So the greatest common factor 7757,8386 is 1.

Lets's calculate LCM of 416,900

Lowest Common Multiple of 416,900 using Common Division

2	416, 900
2	208, 450
	104, 225

∴ So the LCM of the given numbers is 2 x 2 x 104 x 225 = 93600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/93600

Therefore, the GCF of Fractions 7757/416,8386/900 is 1/93600

Least Common Multiple of 416,900 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 416,900 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(416,900) = 4

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

GCF(416,900) x common factors =4 x 1 = 4

LCM(416,900) = ( 416 × 900 ) / 4

LCM(416,900) = 374400 / 4

LCM(416,900) = 93600

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FAQs on GCF of Fractions of 7757/416, 8386/900

1. What is the HCF of 7757,8386?

The HCF of 7757,8386 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 7757/416, 8386/900?

Answer: GCF of Numerators as per given numbers 7757/416, 8386/900 is

GCF of Numerators i.e. for 7757,8386 is 1

LCM of denominators i.e. for 416,900 is 93600.

Thus, GCF of Fractions is 1/93600.Finally, GCF of Fractions for 7757/416, 8386/900 is 1/93600.