How to Find GCF of 392/342, 300/171?

GCF of 392/342, 300/171

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 392/342, 300/171 i.e 4/342 easily. The following is the detailed procedure to determine the greatest common factor of fractions 392/342, 300/171.

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 392/342,300/171?

Given fractions are 392/342,300/171

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 392/342,300/171, numerators are 392,300

Denominators are 342,171

The GCF of 392,300 is 4 .

LCM of 342,171 is 342.

The greatest common factor of 392/342,300/171 = [GCF of 392,300]/[LCM of 342,171]= 4/342

Therefore, the GCF of 392/342,300/171 is 4/342.

Greatest Common Factor of 392,300

To find the highest common factor of 392,300, we have to find the factors of both numbers and list the highest common factor.

The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The HCF of 392,300 is 4.

Lets's calculate GCF of 392,300

Greatest Common Factor (GCF) of 392,300 By Common Division

2	392, 300
2	196, 150
	98, 75

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 392,300 By Matching Biggest Common Factor Method

Now, list down the factors of 392

1,2,4,7,8,14,28,49,56,98,196,392

Now, list down the factors of 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors 392,300 . The biggest common factor number is the GCF number.
So the greatest common factor 392,300 is 4.

Lets's calculate LCM of 342,171

Lowest Common Multiple of 342,171 using Common Division

3	342, 171
3	114, 57
19	38, 19
	2, 1

∴ So the LCM of the given numbers is 3 x 3 x 19 x 2 x 1 = 342

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/342

Therefore, the GCF of Fractions 392/342,300/171 is 4/342

Least Common Multiple of 342,171 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 342,171 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(342,171) = 171

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

GCF(342,171) x common factors =171 x 1 = 171

LCM(342,171) = ( 342 × 171 ) / 171

LCM(342,171) = 58482 / 171

LCM(342,171) = 342

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FAQs on GCF of Fractions of 392/342, 300/171

1. What is the HCF of 392,300?

The HCF of 392,300 is 4

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 392/342, 300/171?

Answer: GCF of Numerators as per given numbers 392/342, 300/171 is

GCF of Numerators i.e. for 392,300 is 4

LCM of denominators i.e. for 342,171 is 342.

Thus, GCF of Fractions is 4/342.Finally, GCF of Fractions for 392/342, 300/171 is 4/342.