How to Find GCF of 16/42, 34/10, 178/32?

GCF of 16/42, 34/10, 178/32

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 16/42, 34/10, 178/32 i.e 2/3360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 16/42, 34/10, 178/32.

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 16/42,34/10,178/32?

Given fractions are 16/42,34/10,178/32

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 16/42,34/10,178/32, numerators are 16,34,178

Denominators are 42,10,32

The GCF of 16,34,178 is 2 .

LCM of 42,10,32 is 3360.

The greatest common factor of 16/42,34/10,178/32 = [GCF of 16,34,178]/[LCM of 42,10,32]= 2/3360

Therefore, the GCF of 16/42,34/10,178/32 is 2/3360.

Greatest Common Factor of 16,34,178

To find the highest common factor of 16,34,178, we have to find the factors of both numbers and list the highest common factor.

The factors of 16 are 1, 2, 4, 8, 16

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

The factors of 178 are 1, 2, 89, 178

The HCF of 16,34,178 is 2.

Lets's calculate GCF of 16,34,178

Greatest Common Factor (GCF) of 16,34,178 By Common Division

2	16, 34, 178
	8, 17, 89

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

Greatest Common Factor of 16,34,178 By Matching Biggest Common Factor Method

Now, list down the factors of 16

1,2,4,8,16

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 178

1,2,89,178

Greatest Common Factor

We found the factors 16,34,178 . The biggest common factor number is the GCF number.
So the greatest common factor 16,34,178 is 2.

Lets's calculate LCM of 42,10,32

Lowest Common Multiple of 42,10,32 using Common Division

2	42, 10, 32
	21, 5, 16

∴ So the LCM of the given numbers is 2 x 21 x 5 x 16 = 3360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3360

Therefore, the GCF of Fractions 16/42,34/10,178/32 is 2/3360

Least Common Multiple of 42,10,32 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 42,10,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,10,32) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(42,10,32) x common factors =2 x 2 = 4

LCM(42,10,32) = ( 42 × 10 × 32 ) / 4

LCM(42,10,32) = 13440 / 4

LCM(42,10,32) = 3360

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FAQs on GCF of Fractions of 16/42, 34/10, 178/32

1. What is the HCF of 16,34,178?

The HCF of 16,34,178 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 16/42, 34/10, 178/32?

Answer: GCF of Numerators as per given numbers 16/42, 34/10, 178/32 is

GCF of Numerators i.e. for 16,34,178 is 2

LCM of denominators i.e. for 42,10,32 is 3360.

Thus, GCF of Fractions is 2/3360.Finally, GCF of Fractions for 16/42, 34/10, 178/32 is 2/3360.