How to Find GCF of 12/689, 67/109, 295/106?

GCF of 12/689, 67/109, 295/106

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 12/689, 67/109, 295/106 i.e 1/150202 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/689, 67/109, 295/106.

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 12/689,67/109,295/106?

Given fractions are 12/689,67/109,295/106

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 12/689,67/109,295/106, numerators are 12,67,295

Denominators are 689,109,106

The GCF of 12,67,295 is 1 .

LCM of 689,109,106 is 150202.

The greatest common factor of 12/689,67/109,295/106 = [GCF of 12,67,295]/[LCM of 689,109,106]= 1/150202

Therefore, the GCF of 12/689,67/109,295/106 is 1/150202.

Greatest Common Factor of 12,67,295

To find the highest common factor of 12,67,295, we have to find the factors of both numbers and list the highest common factor.

The factors of 12 are 1, 2, 3, 4, 6, 12

The factors of 67 are 1, 67

The factors of 295 are 1, 5, 59, 295

The HCF of 12,67,295 is 1.

Lets's calculate GCF of 12,67,295

Greatest Common Factor (GCF) of 12,67,295 By Common Division

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

Greatest Common Factor of 12,67,295 By Matching Biggest Common Factor Method

Now, list down the factors of 12

1,2,3,4,6,12

Now, list down the factors of 67

1,67

Now, list down the factors of 295

1,5,59,295

Greatest Common Factor

We found the factors 12,67,295 . The biggest common factor number is the GCF number.
So the greatest common factor 12,67,295 is 1.

Lets's calculate LCM of 689,109,106

Lowest Common Multiple of 689,109,106 using Common Division

53	689, 109, 106
	13, 109, 2

∴ So the LCM of the given numbers is 53 x 13 x 109 x 2 = 150202

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/150202

Therefore, the GCF of Fractions 12/689,67/109,295/106 is 1/150202

Least Common Multiple of 689,109,106 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 689,109,106 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(689,109,106) = 1

common factors(in case of two or more numbers have common factors) = 53

GCF(689,109,106) x common factors =1 x 53 = 53

LCM(689,109,106) = ( 689 × 109 × 106 ) / 53

LCM(689,109,106) = 7960706 / 53

LCM(689,109,106) = 150202

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 12/689, 67/109, 295/106

1. What is the HCF of 12,67,295?

The HCF of 12,67,295 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 12/689, 67/109, 295/106?

Answer: GCF of Numerators as per given numbers 12/689, 67/109, 295/106 is

GCF of Numerators i.e. for 12,67,295 is 1

LCM of denominators i.e. for 689,109,106 is 150202.

Thus, GCF of Fractions is 1/150202.Finally, GCF of Fractions for 12/689, 67/109, 295/106 is 1/150202.