How to Find GCF of 34/60, 10/62, 322/384?

GCF of 34/60, 10/62, 322/384

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 34/60, 10/62, 322/384 i.e 2/59520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/60, 10/62, 322/384.

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 34/60,10/62,322/384?

Given fractions are 34/60,10/62,322/384

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 34/60,10/62,322/384, numerators are 34,10,322

Denominators are 60,62,384

The GCF of 34,10,322 is 2 .

LCM of 60,62,384 is 59520.

The greatest common factor of 34/60,10/62,322/384 = [GCF of 34,10,322]/[LCM of 60,62,384]= 2/59520

Therefore, the GCF of 34/60,10/62,322/384 is 2/59520.

Greatest Common Factor of 34,10,322

To find the highest common factor of 34,10,322, we have to find the factors of both numbers and list the highest common factor.

The factors of 34 are 1, 2, 17, 34

The factors of 10 are 1, 2, 5, 10

The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322

The HCF of 34,10,322 is 2.

Lets's calculate GCF of 34,10,322

Greatest Common Factor (GCF) of 34,10,322 By Common Division

2	34, 10, 322
	17, 5, 161

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

Greatest Common Factor of 34,10,322 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 322

1,2,7,14,23,46,161,322

Greatest Common Factor

We found the factors 34,10,322 . The biggest common factor number is the GCF number.
So the greatest common factor 34,10,322 is 2.

Lets's calculate LCM of 60,62,384

Lowest Common Multiple of 60,62,384 using Common Division

2	60, 62, 384
2	30, 31, 192
3	15, 31, 96
	5, 31, 32

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 31 x 32 = 59520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/59520

Therefore, the GCF of Fractions 34/60,10/62,322/384 is 2/59520

Least Common Multiple of 60,62,384 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 60,62,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(60,62,384) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(60,62,384) x common factors =2 x 12 = 24

LCM(60,62,384) = ( 60 × 62 × 384 ) / 24

LCM(60,62,384) = 1428480 / 24

LCM(60,62,384) = 59520

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FAQs on GCF of Fractions of 34/60, 10/62, 322/384

1. What is the HCF of 34,10,322?

The HCF of 34,10,322 is 2

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 34/60, 10/62, 322/384?

Answer: GCF of Numerators as per given numbers 34/60, 10/62, 322/384 is

GCF of Numerators i.e. for 34,10,322 is 2

LCM of denominators i.e. for 60,62,384 is 59520.

Thus, GCF of Fractions is 2/59520.Finally, GCF of Fractions for 34/60, 10/62, 322/384 is 2/59520.