GCF of 21/414, 63/978, 476/160
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/414, 63/978, 476/160 i.e 7/5398560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/414, 63/978, 476/160.
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 21/414,63/978,476/160?
Given fractions are 21/414,63/978,476/160
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 21/414,63/978,476/160, numerators are 21,63,476
Denominators are 414,978,160
The GCF of 21,63,476 is 7 .
LCM of 414,978,160 is 5398560.
The greatest common factor of 21/414,63/978,476/160 = [GCF of 21,63,476]/[LCM of 414,978,160]= 7/5398560
Therefore, the GCF of 21/414,63/978,476/160 is 7/5398560.
To find the highest common factor of 21,63,476, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 63 are 1, 3, 7, 9, 21, 63
The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476
The HCF of 21,63,476 is 7.
Lets's calculate GCF of 21,63,476
| 7 | 21, 63, 476 |
| 3, 9, 68 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 21,63,476 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 63
:1,3,7,9,21,63
Now, list down the factors of 476
:1,2,4,7,14,17,28,34,68,119,238,476
Greatest Common Factor
We found the factors 21,63,476 . The biggest common factor number is the GCF number.
So the greatest common factor 21,63,476 is 7.
Lets's calculate LCM of 414,978,160
| 2 | 414, 978, 160 |
| 3 | 207, 489, 80 |
| 69, 163, 80 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 163 x 80 = 5398560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/5398560
Therefore, the GCF of Fractions 21/414,63/978,476/160 is 7/5398560
Least Common Multiple of 414,978,160 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 414,978,160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,978,160) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(414,978,160) x common factors =2 x 6 = 12
LCM(414,978,160) = ( 414 × 978 × 160 ) / 12
LCM(414,978,160) = 64782720 / 12
LCM(414,978,160) = 5398560
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FAQs on GCF of Fractions of 21/414, 63/978, 476/160
1. What is the HCF of 21,63,476?
The HCF of 21,63,476 is 7
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 21/414, 63/978, 476/160?
Answer: GCF of Numerators as per given numbers 21/414, 63/978, 476/160 is
GCF of Numerators i.e. for 21,63,476 is 7
LCM of denominators i.e. for 414,978,160 is 5398560.
Thus, GCF of Fractions is 7/5398560.Finally, GCF of Fractions for 21/414, 63/978, 476/160 is 7/5398560.