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GCF of 617/265, 749/465

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 617/265, 749/465 i.e 1/24645 easily. The following is the detailed procedure to determine the greatest common factor of fractions 617/265, 749/465.

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 617/265,749/465?

Given fractions are 617/265,749/465

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 617/265,749/465, numerators are 617,749

Denominators are 265,465

The GCF of 617,749 is 1 .

LCM of 265,465 is 24645.

The greatest common factor of 617/265,749/465 = [GCF of 617,749]/[LCM of 265,465]= 1/24645

Therefore, the GCF of 617/265,749/465 is 1/24645.

Greatest Common Factor of 617,749

To find the highest common factor of 617,749, we have to find the factors of both numbers and list the highest common factor.

The factors of 617 are 1, 617

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

The HCF of 617,749 is 1.

Lets's calculate GCF of 617,749

Greatest Common Factor (GCF) of 617,749 By Common Division

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

Greatest Common Factor of 617,749 By Matching Biggest Common Factor Method

Greatest Common Factor of 617,749 By Matching Biggest Common Factor Method

Now, list down the factors of 617

:

1,617

Now, list down the factors of 749

:

1,7,107,749

Greatest Common Factor

We found the factors 617,749 . The biggest common factor number is the GCF number.
So the greatest common factor 617,749 is 1.

Lets's calculate LCM of 265,465

Lowest Common Multiple of 265,465 using Common Division

5 265, 465
53, 93

∴ So the LCM of the given numbers is 5 x 53 x 93 = 24645

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/24645

Therefore, the GCF of Fractions 617/265,749/465 is 1/24645

Least Common Multiple of 265,465 with GCF Formula

Least Common Multiple of 265,465 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 265,465 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(265,465) = 5

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

GCF(265,465) x common factors =5 x 1 = 5

LCM(265,465) = ( 265 × 465 ) / 5

LCM(265,465) = 123225 / 5

LCM(265,465) = 24645


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FAQs on GCF of Fractions of 617/265, 749/465

1. What is the HCF of 617,749?

The HCF of 617,749 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 617/265, 749/465?

Answer: GCF of Numerators as per given numbers 617/265, 749/465 is

GCF of Numerators i.e. for 617,749 is 1

LCM of denominators i.e. for 265,465 is 24645.

Thus, GCF of Fractions is 1/24645.Finally, GCF of Fractions for 617/265, 749/465 is 1/24645.