How to Find GCF of 56/42, 144/55, 632/111?

GCF of 56/42, 144/55, 632/111

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 56/42, 144/55, 632/111 i.e 8/85470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 56/42, 144/55, 632/111.

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 56/42,144/55,632/111?

Given fractions are 56/42,144/55,632/111

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 56/42,144/55,632/111, numerators are 56,144,632

Denominators are 42,55,111

The GCF of 56,144,632 is 8 .

LCM of 42,55,111 is 85470.

The greatest common factor of 56/42,144/55,632/111 = [GCF of 56,144,632]/[LCM of 42,55,111]= 8/85470

Therefore, the GCF of 56/42,144/55,632/111 is 8/85470.

Greatest Common Factor of 56,144,632

To find the highest common factor of 56,144,632, we have to find the factors of both numbers and list the highest common factor.

The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

The factors of 632 are 1, 2, 4, 8, 79, 158, 316, 632

The HCF of 56,144,632 is 8.

Lets's calculate GCF of 56,144,632

Greatest Common Factor (GCF) of 56,144,632 By Common Division

2	56, 144, 632
2	28, 72, 316
2	14, 36, 158
	7, 18, 79

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 56,144,632 By Matching Biggest Common Factor Method

Now, list down the factors of 56

1,2,4,7,8,14,28,56

Now, list down the factors of 144

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

Now, list down the factors of 632

1,2,4,8,79,158,316,632

Greatest Common Factor

We found the factors 56,144,632 . The biggest common factor number is the GCF number.
So the greatest common factor 56,144,632 is 8.

Lets's calculate LCM of 42,55,111

Lowest Common Multiple of 42,55,111 using Common Division

3	42, 55, 111
	14, 55, 37

∴ So the LCM of the given numbers is 3 x 14 x 55 x 37 = 85470

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/85470

Therefore, the GCF of Fractions 56/42,144/55,632/111 is 8/85470

Least Common Multiple of 42,55,111 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 42,55,111 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,55,111) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(42,55,111) x common factors =1 x 3 = 3

LCM(42,55,111) = ( 42 × 55 × 111 ) / 3

LCM(42,55,111) = 256410 / 3

LCM(42,55,111) = 85470

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FAQs on GCF of Fractions of 56/42, 144/55, 632/111

1. What is the HCF of 56,144,632?

The HCF of 56,144,632 is 8

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 56/42, 144/55, 632/111?

Answer: GCF of Numerators as per given numbers 56/42, 144/55, 632/111 is

GCF of Numerators i.e. for 56,144,632 is 8

LCM of denominators i.e. for 42,55,111 is 85470.

Thus, GCF of Fractions is 8/85470.Finally, GCF of Fractions for 56/42, 144/55, 632/111 is 8/85470.