How to Find GCF of 672/170, 232/300?

GCF of 672/170, 232/300

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 672/170, 232/300 i.e 8/5100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 672/170, 232/300.

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 672/170,232/300?

Given fractions are 672/170,232/300

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 672/170,232/300, numerators are 672,232

Denominators are 170,300

The GCF of 672,232 is 8 .

LCM of 170,300 is 5100.

The greatest common factor of 672/170,232/300 = [GCF of 672,232]/[LCM of 170,300]= 8/5100

Therefore, the GCF of 672/170,232/300 is 8/5100.

Greatest Common Factor of 672,232

To find the highest common factor of 672,232, we have to find the factors of both numbers and list the highest common factor.

The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672

The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232

The HCF of 672,232 is 8.

Lets's calculate GCF of 672,232

Greatest Common Factor (GCF) of 672,232 By Common Division

2	672, 232
2	336, 116
2	168, 58
	84, 29

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 672,232 By Matching Biggest Common Factor Method

Now, list down the factors of 672

1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,84,96,112,168,224,336,672

Now, list down the factors of 232

1,2,4,8,29,58,116,232

Greatest Common Factor

We found the factors 672,232 . The biggest common factor number is the GCF number.
So the greatest common factor 672,232 is 8.

Lets's calculate LCM of 170,300

Lowest Common Multiple of 170,300 using Common Division

2	170, 300
5	85, 150
	17, 30

∴ So the LCM of the given numbers is 2 x 5 x 17 x 30 = 5100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/5100

Therefore, the GCF of Fractions 672/170,232/300 is 8/5100

Least Common Multiple of 170,300 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 170,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(170,300) = 10

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

GCF(170,300) x common factors =10 x 1 = 10

LCM(170,300) = ( 170 × 300 ) / 10

LCM(170,300) = 51000 / 10

LCM(170,300) = 5100

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FAQs on GCF of Fractions of 672/170, 232/300

1. What is the HCF of 672,232?

The HCF of 672,232 is 8

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 672/170, 232/300?

Answer: GCF of Numerators as per given numbers 672/170, 232/300 is

GCF of Numerators i.e. for 672,232 is 8

LCM of denominators i.e. for 170,300 is 5100.

Thus, GCF of Fractions is 8/5100.Finally, GCF of Fractions for 672/170, 232/300 is 8/5100.