How to Find GCF of 696/32, 120/556?

GCF of 696/32, 120/556

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 696/32, 120/556 i.e 24/4448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 696/32, 120/556.

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 696/32,120/556?

Given fractions are 696/32,120/556

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 696/32,120/556, numerators are 696,120

Denominators are 32,556

The GCF of 696,120 is 24 .

LCM of 32,556 is 4448.

The greatest common factor of 696/32,120/556 = [GCF of 696,120]/[LCM of 32,556]= 24/4448

Therefore, the GCF of 696/32,120/556 is 24/4448.

Greatest Common Factor of 696,120

To find the highest common factor of 696,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 696 are 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The HCF of 696,120 is 24.

Lets's calculate GCF of 696,120

Greatest Common Factor (GCF) of 696,120 By Common Division

2	696, 120
2	348, 60
2	174, 30
3	87, 15
	29, 5

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24

Greatest Common Factor of 696,120 By Matching Biggest Common Factor Method

Now, list down the factors of 696

1,2,3,4,6,8,12,24,29,58,87,116,174,232,348,696

Now, list down the factors of 120

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Greatest Common Factor

We found the factors 696,120 . The biggest common factor number is the GCF number.
So the greatest common factor 696,120 is 24.

Lets's calculate LCM of 32,556

Lowest Common Multiple of 32,556 using Common Division

2	32, 556
2	16, 278
	8, 139

∴ So the LCM of the given numbers is 2 x 2 x 8 x 139 = 4448

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/4448

Therefore, the GCF of Fractions 696/32,120/556 is 24/4448

Least Common Multiple of 32,556 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 32,556 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(32,556) = 4

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

GCF(32,556) x common factors =4 x 1 = 4

LCM(32,556) = ( 32 × 556 ) / 4

LCM(32,556) = 17792 / 4

LCM(32,556) = 4448

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FAQs on GCF of Fractions of 696/32, 120/556

1. What is the HCF of 696,120?

The HCF of 696,120 is 24

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 696/32, 120/556?

Answer: GCF of Numerators as per given numbers 696/32, 120/556 is

GCF of Numerators i.e. for 696,120 is 24

LCM of denominators i.e. for 32,556 is 4448.

Thus, GCF of Fractions is 24/4448.Finally, GCF of Fractions for 696/32, 120/556 is 24/4448.