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GCF of 170/214, 150/299

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 170/214, 150/299 i.e 10/63986 easily. The following is the detailed procedure to determine the greatest common factor of fractions 170/214, 150/299.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 170/214,150/299?

Given fractions are 170/214,150/299

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 170/214,150/299, numerators are 170,150

Denominators are 214,299

The GCF of 170,150 is 10 .

LCM of 214,299 is 63986.

The greatest common factor of 170/214,150/299 = [GCF of 170,150]/[LCM of 214,299]= 10/63986

Therefore, the GCF of 170/214,150/299 is 10/63986.

Greatest Common Factor of 170,150

To find the highest common factor of 170,150, we have to find the factors of both numbers and list the highest common factor.

The factors of 170 are 1, 2, 5, 10, 17, 34, 85, 170

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The HCF of 170,150 is 10.

Lets's calculate GCF of 170,150

Greatest Common Factor (GCF) of 170,150 By Common Division

2 170, 150
5 85, 75
17, 15

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 170,150 By Matching Biggest Common Factor Method

Greatest Common Factor of 170,150 By Matching Biggest Common Factor Method

Now, list down the factors of 170

:

1,2,5,10,17,34,85,170

Now, list down the factors of 150

:

1,2,3,5,6,10,15,25,30,50,75,150

Greatest Common Factor

We found the factors 170,150 . The biggest common factor number is the GCF number.
So the greatest common factor 170,150 is 10.

Lets's calculate LCM of 214,299

Lowest Common Multiple of 214,299 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 63986

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/63986

Therefore, the GCF of Fractions 170/214,150/299 is 10/63986

Least Common Multiple of 214,299 with GCF Formula

Least Common Multiple of 214,299 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 214,299 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,299) = 1

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

GCF(214,299) x common factors =1 x 1 = 1

LCM(214,299) = ( 214 × 299 ) / 1

LCM(214,299) = 63986 / 1

LCM(214,299) = 63986


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FAQs on GCF of Fractions of 170/214, 150/299

1. What is the HCF of 170,150?

The HCF of 170,150 is 10

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 170/214, 150/299?

Answer: GCF of Numerators as per given numbers 170/214, 150/299 is

GCF of Numerators i.e. for 170,150 is 10

LCM of denominators i.e. for 214,299 is 63986.

Thus, GCF of Fractions is 10/63986.Finally, GCF of Fractions for 170/214, 150/299 is 10/63986.