How to Find GCF of 832/34, 864/710?

GCF of 832/34, 864/710

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 832/34, 864/710 i.e 32/12070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 832/34, 864/710.

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 832/34,864/710?

Given fractions are 832/34,864/710

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 832/34,864/710, numerators are 832,864

Denominators are 34,710

The GCF of 832,864 is 32 .

LCM of 34,710 is 12070.

The greatest common factor of 832/34,864/710 = [GCF of 832,864]/[LCM of 34,710]= 32/12070

Therefore, the GCF of 832/34,864/710 is 32/12070.

Greatest Common Factor of 832,864

To find the highest common factor of 832,864, we have to find the factors of both numbers and list the highest common factor.

The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832

The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864

The HCF of 832,864 is 32.

Lets's calculate GCF of 832,864

Greatest Common Factor (GCF) of 832,864 By Common Division

2	832, 864
2	416, 432
2	208, 216
2	104, 108
2	52, 54
	26, 27

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 832,864 By Matching Biggest Common Factor Method

Now, list down the factors of 832

1,2,4,8,13,16,26,32,52,64,104,208,416,832

Now, list down the factors of 864

1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864

Greatest Common Factor

We found the factors 832,864 . The biggest common factor number is the GCF number.
So the greatest common factor 832,864 is 32.

Lets's calculate LCM of 34,710

Lowest Common Multiple of 34,710 using Common Division

2	34, 710
	17, 355

∴ So the LCM of the given numbers is 2 x 17 x 355 = 12070

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/12070

Therefore, the GCF of Fractions 832/34,864/710 is 32/12070

Least Common Multiple of 34,710 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 34,710 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,710) = 2

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

GCF(34,710) x common factors =2 x 1 = 2

LCM(34,710) = ( 34 × 710 ) / 2

LCM(34,710) = 24140 / 2

LCM(34,710) = 12070

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 832/34, 864/710

1. What is the HCF of 832,864?

The HCF of 832,864 is 32

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 832/34, 864/710?

Answer: GCF of Numerators as per given numbers 832/34, 864/710 is

GCF of Numerators i.e. for 832,864 is 32

LCM of denominators i.e. for 34,710 is 12070.

Thus, GCF of Fractions is 32/12070.Finally, GCF of Fractions for 832/34, 864/710 is 32/12070.