How to Find GCF of 1607/334, 1949/171?

GCF of 1607/334, 1949/171

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 1607/334, 1949/171 i.e 1/57114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1607/334, 1949/171.

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 1607/334,1949/171?

Given fractions are 1607/334,1949/171

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 1607/334,1949/171, numerators are 1607,1949

Denominators are 334,171

The GCF of 1607,1949 is 1 .

LCM of 334,171 is 57114.

The greatest common factor of 1607/334,1949/171 = [GCF of 1607,1949]/[LCM of 334,171]= 1/57114

Therefore, the GCF of 1607/334,1949/171 is 1/57114.

Greatest Common Factor of 1607,1949

To find the highest common factor of 1607,1949, we have to find the factors of both numbers and list the highest common factor.

The factors of 1607 are 1, 1607

The factors of 1949 are 1, 1949

The HCF of 1607,1949 is 1.

Lets's calculate GCF of 1607,1949

Greatest Common Factor (GCF) of 1607,1949 By Common Division

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

Greatest Common Factor of 1607,1949 By Matching Biggest Common Factor Method

Now, list down the factors of 1607

1,1607

Now, list down the factors of 1949

1,1949

Greatest Common Factor

We found the factors 1607,1949 . The biggest common factor number is the GCF number.
So the greatest common factor 1607,1949 is 1.

Lets's calculate LCM of 334,171

Lowest Common Multiple of 334,171 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 57114

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/57114

Therefore, the GCF of Fractions 1607/334,1949/171 is 1/57114

Least Common Multiple of 334,171 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 334,171 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(334,171) = 1

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

GCF(334,171) x common factors =1 x 1 = 1

LCM(334,171) = ( 334 × 171 ) / 1

LCM(334,171) = 57114 / 1

LCM(334,171) = 57114

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FAQs on GCF of Fractions of 1607/334, 1949/171

1. What is the HCF of 1607,1949?

The HCF of 1607,1949 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 1607/334, 1949/171?

Answer: GCF of Numerators as per given numbers 1607/334, 1949/171 is

GCF of Numerators i.e. for 1607,1949 is 1

LCM of denominators i.e. for 334,171 is 57114.

Thus, GCF of Fractions is 1/57114.Finally, GCF of Fractions for 1607/334, 1949/171 is 1/57114.