GCF of 1632/282, 7456/213
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1632/282, 7456/213 i.e 32/20022 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1632/282, 7456/213.
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 1632/282,7456/213?
Given fractions are 1632/282,7456/213
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 1632/282,7456/213, numerators are 1632,7456
Denominators are 282,213
The GCF of 1632,7456 is 32 .
LCM of 282,213 is 20022.
The greatest common factor of 1632/282,7456/213 = [GCF of 1632,7456]/[LCM of 282,213]= 32/20022
Therefore, the GCF of 1632/282,7456/213 is 32/20022.
To find the highest common factor of 1632,7456, we have to find the factors of both numbers and list the highest common factor.
The factors of 1632 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96, 102, 136, 204, 272, 408, 544, 816, 1632
The factors of 7456 are 1, 2, 4, 8, 16, 32, 233, 466, 932, 1864, 3728, 7456
The HCF of 1632,7456 is 32.
Lets's calculate GCF of 1632,7456
| 2 | 1632, 7456 |
| 2 | 816, 3728 |
| 2 | 408, 1864 |
| 2 | 204, 932 |
| 2 | 102, 466 |
| 51, 233 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 1632,7456 By Matching Biggest Common Factor Method
Now, list down the factors of 1632
:1,2,3,4,6,8,12,16,17,24,32,34,48,51,68,96,102,136,204,272,408,544,816,1632
Now, list down the factors of 7456
:1,2,4,8,16,32,233,466,932,1864,3728,7456
Greatest Common Factor
We found the factors 1632,7456 . The biggest common factor number is the GCF number.
So the greatest common factor 1632,7456 is 32.
Lets's calculate LCM of 282,213
| 3 | 282, 213 |
| 94, 71 |
∴ So the LCM of the given numbers is 3 x 94 x 71 = 20022
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/20022
Therefore, the GCF of Fractions 1632/282,7456/213 is 32/20022
Least Common Multiple of 282,213 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 282,213 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(282,213) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(282,213) x common factors =3 x 1 = 3
LCM(282,213) = ( 282 × 213 ) / 3
LCM(282,213) = 60066 / 3
LCM(282,213) = 20022
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FAQs on GCF of Fractions of 1632/282, 7456/213
1. What is the HCF of 1632,7456?
The HCF of 1632,7456 is 32
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 1632/282, 7456/213?
Answer: GCF of Numerators as per given numbers 1632/282, 7456/213 is
GCF of Numerators i.e. for 1632,7456 is 32
LCM of denominators i.e. for 282,213 is 20022.
Thus, GCF of Fractions is 32/20022.Finally, GCF of Fractions for 1632/282, 7456/213 is 32/20022.