How to Find GCF of 397/42, 370/1657?

GCF of 397/42, 370/1657

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 397/42, 370/1657 i.e 1/69594 easily. The following is the detailed procedure to determine the greatest common factor of fractions 397/42, 370/1657.

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 397/42,370/1657?

Given fractions are 397/42,370/1657

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 397/42,370/1657, numerators are 397,370

Denominators are 42,1657

The GCF of 397,370 is 1 .

LCM of 42,1657 is 69594.

The greatest common factor of 397/42,370/1657 = [GCF of 397,370]/[LCM of 42,1657]= 1/69594

Therefore, the GCF of 397/42,370/1657 is 1/69594.

Greatest Common Factor of 397,370

To find the highest common factor of 397,370, we have to find the factors of both numbers and list the highest common factor.

The factors of 397 are 1, 397

The factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370

The HCF of 397,370 is 1.

Lets's calculate GCF of 397,370

Greatest Common Factor (GCF) of 397,370 By Common Division

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

Greatest Common Factor of 397,370 By Matching Biggest Common Factor Method

Now, list down the factors of 397

1,397

Now, list down the factors of 370

1,2,5,10,37,74,185,370

Greatest Common Factor

We found the factors 397,370 . The biggest common factor number is the GCF number.
So the greatest common factor 397,370 is 1.

Lets's calculate LCM of 42,1657

Lowest Common Multiple of 42,1657 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 69594

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/69594

Therefore, the GCF of Fractions 397/42,370/1657 is 1/69594

Least Common Multiple of 42,1657 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 42,1657 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,1657) = 1

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

GCF(42,1657) x common factors =1 x 1 = 1

LCM(42,1657) = ( 42 × 1657 ) / 1

LCM(42,1657) = 69594 / 1

LCM(42,1657) = 69594

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FAQs on GCF of Fractions of 397/42, 370/1657

1. What is the HCF of 397,370?

The HCF of 397,370 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 397/42, 370/1657?

Answer: GCF of Numerators as per given numbers 397/42, 370/1657 is

GCF of Numerators i.e. for 397,370 is 1

LCM of denominators i.e. for 42,1657 is 69594.

Thus, GCF of Fractions is 1/69594.Finally, GCF of Fractions for 397/42, 370/1657 is 1/69594.