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GCF of 689/762, 884/165

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 689/762, 884/165 i.e 13/41910 easily. The following is the detailed procedure to determine the greatest common factor of fractions 689/762, 884/165.

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 689/762,884/165?

Given fractions are 689/762,884/165

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 689/762,884/165, numerators are 689,884

Denominators are 762,165

The GCF of 689,884 is 13 .

LCM of 762,165 is 41910.

The greatest common factor of 689/762,884/165 = [GCF of 689,884]/[LCM of 762,165]= 13/41910

Therefore, the GCF of 689/762,884/165 is 13/41910.

Greatest Common Factor of 689,884

To find the highest common factor of 689,884, we have to find the factors of both numbers and list the highest common factor.

The factors of 689 are 1, 13, 53, 689

The factors of 884 are 1, 2, 4, 13, 17, 26, 34, 52, 68, 221, 442, 884

The HCF of 689,884 is 13.

Lets's calculate GCF of 689,884

Greatest Common Factor (GCF) of 689,884 By Common Division

13 689, 884
53, 68

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 689,884 By Matching Biggest Common Factor Method

Greatest Common Factor of 689,884 By Matching Biggest Common Factor Method

Now, list down the factors of 689

:

1,13,53,689

Now, list down the factors of 884

:

1,2,4,13,17,26,34,52,68,221,442,884

Greatest Common Factor

We found the factors 689,884 . The biggest common factor number is the GCF number.
So the greatest common factor 689,884 is 13.

Lets's calculate LCM of 762,165

Lowest Common Multiple of 762,165 using Common Division

3 762, 165
254, 55

∴ So the LCM of the given numbers is 3 x 254 x 55 = 41910

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/41910

Therefore, the GCF of Fractions 689/762,884/165 is 13/41910

Least Common Multiple of 762,165 with GCF Formula

Least Common Multiple of 762,165 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 762,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(762,165) = 3

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

GCF(762,165) x common factors =3 x 1 = 3

LCM(762,165) = ( 762 × 165 ) / 3

LCM(762,165) = 125730 / 3

LCM(762,165) = 41910


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FAQs on GCF of Fractions of 689/762, 884/165

1. What is the HCF of 689,884?

The HCF of 689,884 is 13

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 689/762, 884/165?

Answer: GCF of Numerators as per given numbers 689/762, 884/165 is

GCF of Numerators i.e. for 689,884 is 13

LCM of denominators i.e. for 762,165 is 41910.

Thus, GCF of Fractions is 13/41910.Finally, GCF of Fractions for 689/762, 884/165 is 13/41910.