GCF of 15/14, 37/22, 76/66, 21/32
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 15/14, 37/22, 76/66, 21/32 i.e 1/7392 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/14, 37/22, 76/66, 21/32.
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 15/14,37/22,76/66,21/32?
Given fractions are 15/14,37/22,76/66,21/32
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 15/14,37/22,76/66,21/32, numerators are 15,37,76,21
Denominators are 14,22,66,32
The GCF of 15,37,76,21 is 1 .
LCM of 14,22,66,32 is 7392.
The greatest common factor of 15/14,37/22,76/66,21/32 = [GCF of 15,37,76,21]/[LCM of 14,22,66,32]= 1/7392
Therefore, the GCF of 15/14,37/22,76/66,21/32 is 1/7392.
To find the highest common factor of 15,37,76,21, we have to find the factors of both numbers and list the highest common factor.
The factors of 15 are 1, 3, 5, 15
The factors of 37 are 1, 37
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 21 are 1, 3, 7, 21
The HCF of 15,37,76,21 is 1.
Lets's calculate GCF of 15,37,76,21
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 15,37,76,21 By Matching Biggest Common Factor Method
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 37
:1,37
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 21
:1,3,7,21
Greatest Common Factor
We found the factors 15,37,76,21 . The biggest common factor number is the GCF number.
So the greatest common factor 15,37,76,21 is 1.
Lets's calculate LCM of 14,22,66,32
| 2 | 14, 22, 66, 32 |
| 11 | 7, 11, 33, 16 |
| 7, 1, 3, 16 |
∴ So the LCM of the given numbers is 2 x 11 x 7 x 1 x 3 x 16 = 7392
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7392
Therefore, the GCF of Fractions 15/14,37/22,76/66,21/32 is 1/7392
Least Common Multiple of 14,22,66,32 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 14,22,66,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,22,66,32) = 2
common factors(in case of two or more numbers have common factors) = 44
GCF(14,22,66,32) x common factors =2 x 44 = 88
LCM(14,22,66,32) = ( 14 × 22 × 66 × 32 ) / 88
LCM(14,22,66,32) = 650496 / 88
LCM(14,22,66,32) = 7392
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 15/14, 37/22, 76/66, 21/32
1. What is the HCF of 15,37,76,21?
The HCF of 15,37,76,21 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 15/14, 37/22, 76/66, 21/32?
Answer: GCF of Numerators as per given numbers 15/14, 37/22, 76/66, 21/32 is
GCF of Numerators i.e. for 15,37,76,21 is 1
LCM of denominators i.e. for 14,22,66,32 is 7392.
Thus, GCF of Fractions is 1/7392.Finally, GCF of Fractions for 15/14, 37/22, 76/66, 21/32 is 1/7392.