GCF of 722/78, 432/176
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 722/78, 432/176 i.e 2/6864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 722/78, 432/176.
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 722/78,432/176?
Given fractions are 722/78,432/176
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 722/78,432/176, numerators are 722,432
Denominators are 78,176
The GCF of 722,432 is 2 .
LCM of 78,176 is 6864.
The greatest common factor of 722/78,432/176 = [GCF of 722,432]/[LCM of 78,176]= 2/6864
Therefore, the GCF of 722/78,432/176 is 2/6864.
To find the highest common factor of 722,432, we have to find the factors of both numbers and list the highest common factor.
The factors of 722 are 1, 2, 19, 38, 361, 722
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The HCF of 722,432 is 2.
Lets's calculate GCF of 722,432
| 2 | 722, 432 |
| 361, 216 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 722,432 By Matching Biggest Common Factor Method
Now, list down the factors of 722
:1,2,19,38,361,722
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Greatest Common Factor
We found the factors 722,432 . The biggest common factor number is the GCF number.
So the greatest common factor 722,432 is 2.
Lets's calculate LCM of 78,176
| 2 | 78, 176 |
| 39, 88 |
∴ So the LCM of the given numbers is 2 x 39 x 88 = 6864
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6864
Therefore, the GCF of Fractions 722/78,432/176 is 2/6864
Least Common Multiple of 78,176 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 78,176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,176) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(78,176) x common factors =2 x 1 = 2
LCM(78,176) = ( 78 × 176 ) / 2
LCM(78,176) = 13728 / 2
LCM(78,176) = 6864
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FAQs on GCF of Fractions of 722/78, 432/176
1. What is the HCF of 722,432?
The HCF of 722,432 is 2
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 722/78, 432/176?
Answer: GCF of Numerators as per given numbers 722/78, 432/176 is
GCF of Numerators i.e. for 722,432 is 2
LCM of denominators i.e. for 78,176 is 6864.
Thus, GCF of Fractions is 2/6864.Finally, GCF of Fractions for 722/78, 432/176 is 2/6864.