How to Find GCF of 1406/349, 5563/674?

GCF of 1406/349, 5563/674

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 1406/349, 5563/674 i.e 1/235226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1406/349, 5563/674.

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 1406/349,5563/674?

Given fractions are 1406/349,5563/674

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 1406/349,5563/674, numerators are 1406,5563

Denominators are 349,674

The GCF of 1406,5563 is 1 .

LCM of 349,674 is 235226.

The greatest common factor of 1406/349,5563/674 = [GCF of 1406,5563]/[LCM of 349,674]= 1/235226

Therefore, the GCF of 1406/349,5563/674 is 1/235226.

Greatest Common Factor of 1406,5563

To find the highest common factor of 1406,5563, we have to find the factors of both numbers and list the highest common factor.

The factors of 1406 are 1, 2, 19, 37, 38, 74, 703, 1406

The factors of 5563 are 1, 5563

The HCF of 1406,5563 is 1.

Lets's calculate GCF of 1406,5563

Greatest Common Factor (GCF) of 1406,5563 By Common Division

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

Greatest Common Factor of 1406,5563 By Matching Biggest Common Factor Method

Now, list down the factors of 1406

1,2,19,37,38,74,703,1406

Now, list down the factors of 5563

1,5563

Greatest Common Factor

We found the factors 1406,5563 . The biggest common factor number is the GCF number.
So the greatest common factor 1406,5563 is 1.

Lets's calculate LCM of 349,674

Lowest Common Multiple of 349,674 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 235226

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/235226

Therefore, the GCF of Fractions 1406/349,5563/674 is 1/235226

Least Common Multiple of 349,674 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 349,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(349,674) = 1

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

GCF(349,674) x common factors =1 x 1 = 1

LCM(349,674) = ( 349 × 674 ) / 1

LCM(349,674) = 235226 / 1

LCM(349,674) = 235226

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FAQs on GCF of Fractions of 1406/349, 5563/674

1. What is the HCF of 1406,5563?

The HCF of 1406,5563 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 1406/349, 5563/674?

Answer: GCF of Numerators as per given numbers 1406/349, 5563/674 is

GCF of Numerators i.e. for 1406,5563 is 1

LCM of denominators i.e. for 349,674 is 235226.

Thus, GCF of Fractions is 1/235226.Finally, GCF of Fractions for 1406/349, 5563/674 is 1/235226.