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GCF of 34/160, 32/1731

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 34/160, 32/1731 i.e 2/276960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/160, 32/1731.

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 34/160,32/1731?

Given fractions are 34/160,32/1731

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 34/160,32/1731, numerators are 34,32

Denominators are 160,1731

The GCF of 34,32 is 2 .

LCM of 160,1731 is 276960.

The greatest common factor of 34/160,32/1731 = [GCF of 34,32]/[LCM of 160,1731]= 2/276960

Therefore, the GCF of 34/160,32/1731 is 2/276960.

Greatest Common Factor of 34,32

To find the highest common factor of 34,32, we have to find the factors of both numbers and list the highest common factor.

The factors of 34 are 1, 2, 17, 34

The factors of 32 are 1, 2, 4, 8, 16, 32

The HCF of 34,32 is 2.

Lets's calculate GCF of 34,32

Greatest Common Factor (GCF) of 34,32 By Common Division

2 34, 32
17, 16

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 34,32 By Matching Biggest Common Factor Method

Greatest Common Factor of 34,32 By Matching Biggest Common Factor Method

Now, list down the factors of 34

:

1,2,17,34

Now, list down the factors of 32

:

1,2,4,8,16,32

Greatest Common Factor

We found the factors 34,32 . The biggest common factor number is the GCF number.
So the greatest common factor 34,32 is 2.

Lets's calculate LCM of 160,1731

Lowest Common Multiple of 160,1731 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 276960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/276960

Therefore, the GCF of Fractions 34/160,32/1731 is 2/276960

Least Common Multiple of 160,1731 with GCF Formula

Least Common Multiple of 160,1731 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 160,1731 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(160,1731) = 1

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

GCF(160,1731) x common factors =1 x 1 = 1

LCM(160,1731) = ( 160 × 1731 ) / 1

LCM(160,1731) = 276960 / 1

LCM(160,1731) = 276960


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FAQs on GCF of Fractions of 34/160, 32/1731

1. What is the HCF of 34,32?

The HCF of 34,32 is 2

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 34/160, 32/1731?

Answer: GCF of Numerators as per given numbers 34/160, 32/1731 is

GCF of Numerators i.e. for 34,32 is 2

LCM of denominators i.e. for 160,1731 is 276960.

Thus, GCF of Fractions is 2/276960.Finally, GCF of Fractions for 34/160, 32/1731 is 2/276960.