How to Find GCF of 5035/416, 7657/1549?

GCF of 5035/416, 7657/1549

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 5035/416, 7657/1549 i.e 19/644384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5035/416, 7657/1549.

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 5035/416,7657/1549?

Given fractions are 5035/416,7657/1549

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 5035/416,7657/1549, numerators are 5035,7657

Denominators are 416,1549

The GCF of 5035,7657 is 19 .

LCM of 416,1549 is 644384.

The greatest common factor of 5035/416,7657/1549 = [GCF of 5035,7657]/[LCM of 416,1549]= 19/644384

Therefore, the GCF of 5035/416,7657/1549 is 19/644384.

Greatest Common Factor of 5035,7657

To find the highest common factor of 5035,7657, we have to find the factors of both numbers and list the highest common factor.

The factors of 5035 are 1, 5, 19, 53, 95, 265, 1007, 5035

The factors of 7657 are 1, 13, 19, 31, 247, 403, 589, 7657

The HCF of 5035,7657 is 19.

Lets's calculate GCF of 5035,7657

Greatest Common Factor (GCF) of 5035,7657 By Common Division

19	5035, 7657
	265, 403

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 5035,7657 By Matching Biggest Common Factor Method

Now, list down the factors of 5035

1,5,19,53,95,265,1007,5035

Now, list down the factors of 7657

1,13,19,31,247,403,589,7657

Greatest Common Factor

We found the factors 5035,7657 . The biggest common factor number is the GCF number.
So the greatest common factor 5035,7657 is 19.

Lets's calculate LCM of 416,1549

Lowest Common Multiple of 416,1549 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 644384

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/644384

Therefore, the GCF of Fractions 5035/416,7657/1549 is 19/644384

Least Common Multiple of 416,1549 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 416,1549 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(416,1549) = 1

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

GCF(416,1549) x common factors =1 x 1 = 1

LCM(416,1549) = ( 416 × 1549 ) / 1

LCM(416,1549) = 644384 / 1

LCM(416,1549) = 644384

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FAQs on GCF of Fractions of 5035/416, 7657/1549

1. What is the HCF of 5035,7657?

The HCF of 5035,7657 is 19

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 5035/416, 7657/1549?

Answer: GCF of Numerators as per given numbers 5035/416, 7657/1549 is

GCF of Numerators i.e. for 5035,7657 is 19

LCM of denominators i.e. for 416,1549 is 644384.

Thus, GCF of Fractions is 19/644384.Finally, GCF of Fractions for 5035/416, 7657/1549 is 19/644384.