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GCF of 223/746, 306/170

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 223/746, 306/170 i.e 1/63410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 223/746, 306/170.

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 223/746,306/170?

Given fractions are 223/746,306/170

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 223/746,306/170, numerators are 223,306

Denominators are 746,170

The GCF of 223,306 is 1 .

LCM of 746,170 is 63410.

The greatest common factor of 223/746,306/170 = [GCF of 223,306]/[LCM of 746,170]= 1/63410

Therefore, the GCF of 223/746,306/170 is 1/63410.

Greatest Common Factor of 223,306

To find the highest common factor of 223,306, we have to find the factors of both numbers and list the highest common factor.

The factors of 223 are 1, 223

The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

The HCF of 223,306 is 1.

Lets's calculate GCF of 223,306

Greatest Common Factor (GCF) of 223,306 By Common Division

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

Greatest Common Factor of 223,306 By Matching Biggest Common Factor Method

Greatest Common Factor of 223,306 By Matching Biggest Common Factor Method

Now, list down the factors of 223

:

1,223

Now, list down the factors of 306

:

1,2,3,6,9,17,18,34,51,102,153,306

Greatest Common Factor

We found the factors 223,306 . The biggest common factor number is the GCF number.
So the greatest common factor 223,306 is 1.

Lets's calculate LCM of 746,170

Lowest Common Multiple of 746,170 using Common Division

2 746, 170
373, 85

∴ So the LCM of the given numbers is 2 x 373 x 85 = 63410

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/63410

Therefore, the GCF of Fractions 223/746,306/170 is 1/63410

Least Common Multiple of 746,170 with GCF Formula

Least Common Multiple of 746,170 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 746,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(746,170) = 2

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

GCF(746,170) x common factors =2 x 1 = 2

LCM(746,170) = ( 746 × 170 ) / 2

LCM(746,170) = 126820 / 2

LCM(746,170) = 63410


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FAQs on GCF of Fractions of 223/746, 306/170

1. What is the HCF of 223,306?

The HCF of 223,306 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 223/746, 306/170?

Answer: GCF of Numerators as per given numbers 223/746, 306/170 is

GCF of Numerators i.e. for 223,306 is 1

LCM of denominators i.e. for 746,170 is 63410.

Thus, GCF of Fractions is 1/63410.Finally, GCF of Fractions for 223/746, 306/170 is 1/63410.