How to Find GCF of 42/600, 529/714, 827/120?

GCF of 42/600, 529/714, 827/120

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 42/600, 529/714, 827/120 i.e 1/71400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/600, 529/714, 827/120.

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 42/600,529/714,827/120?

Given fractions are 42/600,529/714,827/120

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 42/600,529/714,827/120, numerators are 42,529,827

Denominators are 600,714,120

The GCF of 42,529,827 is 1 .

LCM of 600,714,120 is 71400.

The greatest common factor of 42/600,529/714,827/120 = [GCF of 42,529,827]/[LCM of 600,714,120]= 1/71400

Therefore, the GCF of 42/600,529/714,827/120 is 1/71400.

Greatest Common Factor of 42,529,827

To find the highest common factor of 42,529,827, we have to find the factors of both numbers and list the highest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 529 are 1, 23, 529

The factors of 827 are 1, 827

The HCF of 42,529,827 is 1.

Lets's calculate GCF of 42,529,827

Greatest Common Factor (GCF) of 42,529,827 By Common Division

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

Greatest Common Factor of 42,529,827 By Matching Biggest Common Factor Method

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Now, list down the factors of 529

1,23,529

Now, list down the factors of 827

1,827

Greatest Common Factor

We found the factors 42,529,827 . The biggest common factor number is the GCF number.
So the greatest common factor 42,529,827 is 1.

Lets's calculate LCM of 600,714,120

Lowest Common Multiple of 600,714,120 using Common Division

2	600, 714, 120
2	300, 357, 60
2	150, 357, 30
3	75, 357, 15
5	25, 119, 5
	1, 119, 5

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 119 x 5 = 71400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/71400

Therefore, the GCF of Fractions 42/600,529/714,827/120 is 1/71400

Least Common Multiple of 600,714,120 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 600,714,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(600,714,120) = 6

common factors(in case of two or more numbers have common factors) = 120

GCF(600,714,120) x common factors =6 x 120 = 720

LCM(600,714,120) = ( 600 × 714 × 120 ) / 720

LCM(600,714,120) = 51408000 / 720

LCM(600,714,120) = 71400

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FAQs on GCF of Fractions of 42/600, 529/714, 827/120

1. What is the HCF of 42,529,827?

The HCF of 42,529,827 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 42/600, 529/714, 827/120?

Answer: GCF of Numerators as per given numbers 42/600, 529/714, 827/120 is

GCF of Numerators i.e. for 42,529,827 is 1

LCM of denominators i.e. for 600,714,120 is 71400.

Thus, GCF of Fractions is 1/71400.Finally, GCF of Fractions for 42/600, 529/714, 827/120 is 1/71400.