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GCF of 749/15, 308/637

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 749/15, 308/637 i.e 7/9555 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/15, 308/637.

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 749/15,308/637?

Given fractions are 749/15,308/637

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 749/15,308/637, numerators are 749,308

Denominators are 15,637

The GCF of 749,308 is 7 .

LCM of 15,637 is 9555.

The greatest common factor of 749/15,308/637 = [GCF of 749,308]/[LCM of 15,637]= 7/9555

Therefore, the GCF of 749/15,308/637 is 7/9555.

Greatest Common Factor of 749,308

To find the highest common factor of 749,308, we have to find the factors of both numbers and list the highest common factor.

The factors of 749 are 1, 7, 107, 749

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The HCF of 749,308 is 7.

Lets's calculate GCF of 749,308

Greatest Common Factor (GCF) of 749,308 By Common Division

7 749, 308
107, 44

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

Greatest Common Factor of 749,308 By Matching Biggest Common Factor Method

Greatest Common Factor of 749,308 By Matching Biggest Common Factor Method

Now, list down the factors of 749

:

1,7,107,749

Now, list down the factors of 308

:

1,2,4,7,11,14,22,28,44,77,154,308

Greatest Common Factor

We found the factors 749,308 . The biggest common factor number is the GCF number.
So the greatest common factor 749,308 is 7.

Lets's calculate LCM of 15,637

Lowest Common Multiple of 15,637 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9555

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/9555

Therefore, the GCF of Fractions 749/15,308/637 is 7/9555

Least Common Multiple of 15,637 with GCF Formula

Least Common Multiple of 15,637 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 15,637 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(15,637) = 1

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

GCF(15,637) x common factors =1 x 1 = 1

LCM(15,637) = ( 15 × 637 ) / 1

LCM(15,637) = 9555 / 1

LCM(15,637) = 9555


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FAQs on GCF of Fractions of 749/15, 308/637

1. What is the HCF of 749,308?

The HCF of 749,308 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 749/15, 308/637?

Answer: GCF of Numerators as per given numbers 749/15, 308/637 is

GCF of Numerators i.e. for 749,308 is 7

LCM of denominators i.e. for 15,637 is 9555.

Thus, GCF of Fractions is 7/9555.Finally, GCF of Fractions for 749/15, 308/637 is 7/9555.