GCF of 71/32, 472/27, 318/224
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 71/32, 472/27, 318/224 i.e 1/6048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/32, 472/27, 318/224.
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 71/32,472/27,318/224?
Given fractions are 71/32,472/27,318/224
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 71/32,472/27,318/224, numerators are 71,472,318
Denominators are 32,27,224
The GCF of 71,472,318 is 1 .
LCM of 32,27,224 is 6048.
The greatest common factor of 71/32,472/27,318/224 = [GCF of 71,472,318]/[LCM of 32,27,224]= 1/6048
Therefore, the GCF of 71/32,472/27,318/224 is 1/6048.
To find the highest common factor of 71,472,318, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 472 are 1, 2, 4, 8, 59, 118, 236, 472
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318
The HCF of 71,472,318 is 1.
Lets's calculate GCF of 71,472,318
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 71,472,318 By Matching Biggest Common Factor Method
Now, list down the factors of 71
:1,71
Now, list down the factors of 472
:1,2,4,8,59,118,236,472
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
Greatest Common Factor
We found the factors 71,472,318 . The biggest common factor number is the GCF number.
So the greatest common factor 71,472,318 is 1.
Lets's calculate LCM of 32,27,224
| 2 | 32, 27, 224 |
| 2 | 16, 27, 112 |
| 2 | 8, 27, 56 |
| 2 | 4, 27, 28 |
| 2 | 2, 27, 14 |
| 1, 27, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 1 x 27 x 7 = 6048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6048
Therefore, the GCF of Fractions 71/32,472/27,318/224 is 1/6048
Least Common Multiple of 32,27,224 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 32,27,224 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,27,224) = 1
common factors(in case of two or more numbers have common factors) = 32
GCF(32,27,224) x common factors =1 x 32 = 32
LCM(32,27,224) = ( 32 × 27 × 224 ) / 32
LCM(32,27,224) = 193536 / 32
LCM(32,27,224) = 6048
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FAQs on GCF of Fractions of 71/32, 472/27, 318/224
1. What is the HCF of 71,472,318?
The HCF of 71,472,318 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 71/32, 472/27, 318/224?
Answer: GCF of Numerators as per given numbers 71/32, 472/27, 318/224 is
GCF of Numerators i.e. for 71,472,318 is 1
LCM of denominators i.e. for 32,27,224 is 6048.
Thus, GCF of Fractions is 1/6048.Finally, GCF of Fractions for 71/32, 472/27, 318/224 is 1/6048.