How to Find GCF of 1732/472, 1752/221?

GCF of 1732/472, 1752/221

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 1732/472, 1752/221 i.e 4/104312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1732/472, 1752/221.

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 1732/472,1752/221?

Given fractions are 1732/472,1752/221

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 1732/472,1752/221, numerators are 1732,1752

Denominators are 472,221

The GCF of 1732,1752 is 4 .

LCM of 472,221 is 104312.

The greatest common factor of 1732/472,1752/221 = [GCF of 1732,1752]/[LCM of 472,221]= 4/104312

Therefore, the GCF of 1732/472,1752/221 is 4/104312.

Greatest Common Factor of 1732,1752

To find the highest common factor of 1732,1752, we have to find the factors of both numbers and list the highest common factor.

The factors of 1732 are 1, 2, 4, 433, 866, 1732

The factors of 1752 are 1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876, 1752

The HCF of 1732,1752 is 4.

Lets's calculate GCF of 1732,1752

Greatest Common Factor (GCF) of 1732,1752 By Common Division

2	1732, 1752
2	866, 876
	433, 438

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 1732,1752 By Matching Biggest Common Factor Method

Now, list down the factors of 1732

1,2,4,433,866,1732

Now, list down the factors of 1752

1,2,3,4,6,8,12,24,73,146,219,292,438,584,876,1752

Greatest Common Factor

We found the factors 1732,1752 . The biggest common factor number is the GCF number.
So the greatest common factor 1732,1752 is 4.

Lets's calculate LCM of 472,221

Lowest Common Multiple of 472,221 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 104312

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/104312

Therefore, the GCF of Fractions 1732/472,1752/221 is 4/104312

Least Common Multiple of 472,221 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 472,221 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(472,221) = 1

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

GCF(472,221) x common factors =1 x 1 = 1

LCM(472,221) = ( 472 × 221 ) / 1

LCM(472,221) = 104312 / 1

LCM(472,221) = 104312

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FAQs on GCF of Fractions of 1732/472, 1752/221

1. What is the HCF of 1732,1752?

The HCF of 1732,1752 is 4

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 1732/472, 1752/221?

Answer: GCF of Numerators as per given numbers 1732/472, 1752/221 is

GCF of Numerators i.e. for 1732,1752 is 4

LCM of denominators i.e. for 472,221 is 104312.

Thus, GCF of Fractions is 4/104312.Finally, GCF of Fractions for 1732/472, 1752/221 is 4/104312.