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GCF of 169/64, 561/338

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 169/64, 561/338 i.e 1/10816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 169/64, 561/338.

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 169/64,561/338?

Given fractions are 169/64,561/338

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 169/64,561/338, numerators are 169,561

Denominators are 64,338

The GCF of 169,561 is 1 .

LCM of 64,338 is 10816.

The greatest common factor of 169/64,561/338 = [GCF of 169,561]/[LCM of 64,338]= 1/10816

Therefore, the GCF of 169/64,561/338 is 1/10816.

Greatest Common Factor of 169,561

To find the highest common factor of 169,561, we have to find the factors of both numbers and list the highest common factor.

The factors of 169 are 1, 13, 169

The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561

The HCF of 169,561 is 1.

Lets's calculate GCF of 169,561

Greatest Common Factor (GCF) of 169,561 By Common Division

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

Greatest Common Factor of 169,561 By Matching Biggest Common Factor Method

Greatest Common Factor of 169,561 By Matching Biggest Common Factor Method

Now, list down the factors of 169

:

1,13,169

Now, list down the factors of 561

:

1,3,11,17,33,51,187,561

Greatest Common Factor

We found the factors 169,561 . The biggest common factor number is the GCF number.
So the greatest common factor 169,561 is 1.

Lets's calculate LCM of 64,338

Lowest Common Multiple of 64,338 using Common Division

2 64, 338
32, 169

∴ So the LCM of the given numbers is 2 x 32 x 169 = 10816

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10816

Therefore, the GCF of Fractions 169/64,561/338 is 1/10816

Least Common Multiple of 64,338 with GCF Formula

Least Common Multiple of 64,338 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 64,338 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,338) = 2

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

GCF(64,338) x common factors =2 x 1 = 2

LCM(64,338) = ( 64 × 338 ) / 2

LCM(64,338) = 21632 / 2

LCM(64,338) = 10816


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FAQs on GCF of Fractions of 169/64, 561/338

1. What is the HCF of 169,561?

The HCF of 169,561 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 169/64, 561/338?

Answer: GCF of Numerators as per given numbers 169/64, 561/338 is

GCF of Numerators i.e. for 169,561 is 1

LCM of denominators i.e. for 64,338 is 10816.

Thus, GCF of Fractions is 1/10816.Finally, GCF of Fractions for 169/64, 561/338 is 1/10816.