How to Find GCF of 63/68, 66/65, 126/16?

GCF of 63/68, 66/65, 126/16

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 63/68, 66/65, 126/16 i.e 3/17680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 63/68, 66/65, 126/16.

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 63/68,66/65,126/16?

Given fractions are 63/68,66/65,126/16

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 63/68,66/65,126/16, numerators are 63,66,126

Denominators are 68,65,16

The GCF of 63,66,126 is 3 .

LCM of 68,65,16 is 17680.

The greatest common factor of 63/68,66/65,126/16 = [GCF of 63,66,126]/[LCM of 68,65,16]= 3/17680

Therefore, the GCF of 63/68,66/65,126/16 is 3/17680.

Greatest Common Factor of 63,66,126

To find the highest common factor of 63,66,126, we have to find the factors of both numbers and list the highest common factor.

The factors of 63 are 1, 3, 7, 9, 21, 63

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66

The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

The HCF of 63,66,126 is 3.

Lets's calculate GCF of 63,66,126

Greatest Common Factor (GCF) of 63,66,126 By Common Division

3	63, 66, 126
	21, 22, 42

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 63,66,126 By Matching Biggest Common Factor Method

Now, list down the factors of 63

1,3,7,9,21,63

Now, list down the factors of 66

1,2,3,6,11,22,33,66

Now, list down the factors of 126

1,2,3,6,7,9,14,18,21,42,63,126

Greatest Common Factor

We found the factors 63,66,126 . The biggest common factor number is the GCF number.
So the greatest common factor 63,66,126 is 3.

Lets's calculate LCM of 68,65,16

Lowest Common Multiple of 68,65,16 using Common Division

2	68, 65, 16
2	34, 65, 8
	17, 65, 4

∴ So the LCM of the given numbers is 2 x 2 x 17 x 65 x 4 = 17680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/17680

Therefore, the GCF of Fractions 63/68,66/65,126/16 is 3/17680

Least Common Multiple of 68,65,16 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 68,65,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,65,16) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(68,65,16) x common factors =1 x 4 = 4

LCM(68,65,16) = ( 68 × 65 × 16 ) / 4

LCM(68,65,16) = 70720 / 4

LCM(68,65,16) = 17680

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FAQs on GCF of Fractions of 63/68, 66/65, 126/16

1. What is the HCF of 63,66,126?

The HCF of 63,66,126 is 3

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 63/68, 66/65, 126/16?

Answer: GCF of Numerators as per given numbers 63/68, 66/65, 126/16 is

GCF of Numerators i.e. for 63,66,126 is 3

LCM of denominators i.e. for 68,65,16 is 17680.

Thus, GCF of Fractions is 3/17680.Finally, GCF of Fractions for 63/68, 66/65, 126/16 is 3/17680.