GCF of 40/47, 45/14, 17/21, 70/336
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/47, 45/14, 17/21, 70/336 i.e 1/15792 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/47, 45/14, 17/21, 70/336.
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 40/47,45/14,17/21,70/336?
Given fractions are 40/47,45/14,17/21,70/336
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 40/47,45/14,17/21,70/336, numerators are 40,45,17,70
Denominators are 47,14,21,336
The GCF of 40,45,17,70 is 1 .
LCM of 47,14,21,336 is 15792.
The greatest common factor of 40/47,45/14,17/21,70/336 = [GCF of 40,45,17,70]/[LCM of 47,14,21,336]= 1/15792
Therefore, the GCF of 40/47,45/14,17/21,70/336 is 1/15792.
To find the highest common factor of 40,45,17,70, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 17 are 1, 17
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The HCF of 40,45,17,70 is 1.
Lets's calculate GCF of 40,45,17,70
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,45,17,70 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 17
:1,17
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Greatest Common Factor
We found the factors 40,45,17,70 . The biggest common factor number is the GCF number.
So the greatest common factor 40,45,17,70 is 1.
Lets's calculate LCM of 47,14,21,336
| 2 | 47, 14, 21, 336 |
| 3 | 47, 7, 21, 168 |
| 7 | 47, 7, 7, 56 |
| 47, 1, 1, 8 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 47 x 1 x 1 x 8 = 15792
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15792
Therefore, the GCF of Fractions 40/47,45/14,17/21,70/336 is 1/15792
Least Common Multiple of 47,14,21,336 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 47,14,21,336 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(47,14,21,336) = 1
common factors(in case of two or more numbers have common factors) = 294
GCF(47,14,21,336) x common factors =1 x 294 = 294
LCM(47,14,21,336) = ( 47 × 14 × 21 × 336 ) / 294
LCM(47,14,21,336) = 4642848 / 294
LCM(47,14,21,336) = 15792
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 40/47, 45/14, 17/21, 70/336
1. What is the HCF of 40,45,17,70?
The HCF of 40,45,17,70 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 40/47, 45/14, 17/21, 70/336?
Answer: GCF of Numerators as per given numbers 40/47, 45/14, 17/21, 70/336 is
GCF of Numerators i.e. for 40,45,17,70 is 1
LCM of denominators i.e. for 47,14,21,336 is 15792.
Thus, GCF of Fractions is 1/15792.Finally, GCF of Fractions for 40/47, 45/14, 17/21, 70/336 is 1/15792.