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GCF of 402/120, 349/675

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 402/120, 349/675 i.e 1/5400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 402/120, 349/675.

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 402/120,349/675?

Given fractions are 402/120,349/675

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 402/120,349/675, numerators are 402,349

Denominators are 120,675

The GCF of 402,349 is 1 .

LCM of 120,675 is 5400.

The greatest common factor of 402/120,349/675 = [GCF of 402,349]/[LCM of 120,675]= 1/5400

Therefore, the GCF of 402/120,349/675 is 1/5400.

Greatest Common Factor of 402,349

To find the highest common factor of 402,349, we have to find the factors of both numbers and list the highest common factor.

The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402

The factors of 349 are 1, 349

The HCF of 402,349 is 1.

Lets's calculate GCF of 402,349

Greatest Common Factor (GCF) of 402,349 By Common Division

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

Greatest Common Factor of 402,349 By Matching Biggest Common Factor Method

Greatest Common Factor of 402,349 By Matching Biggest Common Factor Method

Now, list down the factors of 402

:

1,2,3,6,67,134,201,402

Now, list down the factors of 349

:

1,349

Greatest Common Factor

We found the factors 402,349 . The biggest common factor number is the GCF number.
So the greatest common factor 402,349 is 1.

Lets's calculate LCM of 120,675

Lowest Common Multiple of 120,675 using Common Division

3 120, 675
5 40, 225
8, 45

∴ So the LCM of the given numbers is 3 x 5 x 8 x 45 = 5400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5400

Therefore, the GCF of Fractions 402/120,349/675 is 1/5400

Least Common Multiple of 120,675 with GCF Formula

Least Common Multiple of 120,675 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 120,675 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(120,675) = 15

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

GCF(120,675) x common factors =15 x 1 = 15

LCM(120,675) = ( 120 × 675 ) / 15

LCM(120,675) = 81000 / 15

LCM(120,675) = 5400


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FAQs on GCF of Fractions of 402/120, 349/675

1. What is the HCF of 402,349?

The HCF of 402,349 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 402/120, 349/675?

Answer: GCF of Numerators as per given numbers 402/120, 349/675 is

GCF of Numerators i.e. for 402,349 is 1

LCM of denominators i.e. for 120,675 is 5400.

Thus, GCF of Fractions is 1/5400.Finally, GCF of Fractions for 402/120, 349/675 is 1/5400.