How to Find GCF of 253/365, 7774/918?

GCF of 253/365, 7774/918

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 253/365, 7774/918 i.e 23/335070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 253/365, 7774/918.

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 253/365,7774/918?

Given fractions are 253/365,7774/918

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 253/365,7774/918, numerators are 253,7774

Denominators are 365,918

The GCF of 253,7774 is 23 .

LCM of 365,918 is 335070.

The greatest common factor of 253/365,7774/918 = [GCF of 253,7774]/[LCM of 365,918]= 23/335070

Therefore, the GCF of 253/365,7774/918 is 23/335070.

Greatest Common Factor of 253,7774

To find the highest common factor of 253,7774, we have to find the factors of both numbers and list the highest common factor.

The factors of 253 are 1, 11, 23, 253

The factors of 7774 are 1, 2, 13, 23, 26, 46, 169, 299, 338, 598, 3887, 7774

The HCF of 253,7774 is 23.

Lets's calculate GCF of 253,7774

Greatest Common Factor (GCF) of 253,7774 By Common Division

23	253, 7774
	11, 338

∴ So the GCF of the given numbers is 23 = 23

Greatest Common Factor of 253,7774 By Matching Biggest Common Factor Method

Now, list down the factors of 253

1,11,23,253

Now, list down the factors of 7774

1,2,13,23,26,46,169,299,338,598,3887,7774

Greatest Common Factor

We found the factors 253,7774 . The biggest common factor number is the GCF number.
So the greatest common factor 253,7774 is 23.

Lets's calculate LCM of 365,918

Lowest Common Multiple of 365,918 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 335070

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/335070

Therefore, the GCF of Fractions 253/365,7774/918 is 23/335070

Least Common Multiple of 365,918 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 365,918 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(365,918) = 1

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

GCF(365,918) x common factors =1 x 1 = 1

LCM(365,918) = ( 365 × 918 ) / 1

LCM(365,918) = 335070 / 1

LCM(365,918) = 335070

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FAQs on GCF of Fractions of 253/365, 7774/918

1. What is the HCF of 253,7774?

The HCF of 253,7774 is 23

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 253/365, 7774/918?

Answer: GCF of Numerators as per given numbers 253/365, 7774/918 is

GCF of Numerators i.e. for 253,7774 is 23

LCM of denominators i.e. for 365,918 is 335070.

Thus, GCF of Fractions is 23/335070.Finally, GCF of Fractions for 253/365, 7774/918 is 23/335070.