GCF of 8/40, 32/73, 84/964, 970/513
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/40, 32/73, 84/964, 970/513 i.e 2/361008360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/40, 32/73, 84/964, 970/513.
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 8/40,32/73,84/964,970/513?
Given fractions are 8/40,32/73,84/964,970/513
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 8/40,32/73,84/964,970/513, numerators are 8,32,84,970
Denominators are 40,73,964,513
The GCF of 8,32,84,970 is 2 .
LCM of 40,73,964,513 is 361008360.
The greatest common factor of 8/40,32/73,84/964,970/513 = [GCF of 8,32,84,970]/[LCM of 40,73,964,513]= 2/361008360
Therefore, the GCF of 8/40,32/73,84/964,970/513 is 2/361008360.
To find the highest common factor of 8,32,84,970, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 970 are 1, 2, 5, 10, 97, 194, 485, 970
The HCF of 8,32,84,970 is 2.
Lets's calculate GCF of 8,32,84,970
| 2 | 8, 32, 84, 970 |
| 4, 16, 42, 485 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8,32,84,970 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 970
:1,2,5,10,97,194,485,970
Greatest Common Factor
We found the factors 8,32,84,970 . The biggest common factor number is the GCF number.
So the greatest common factor 8,32,84,970 is 2.
Lets's calculate LCM of 40,73,964,513
| 2 | 40, 73, 964, 513 |
| 2 | 20, 73, 482, 513 |
| 10, 73, 241, 513 |
∴ So the LCM of the given numbers is 2 x 2 x 10 x 73 x 241 x 513 = 361008360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/361008360
Therefore, the GCF of Fractions 8/40,32/73,84/964,970/513 is 2/361008360
Least Common Multiple of 40,73,964,513 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 40,73,964,513 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,73,964,513) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(40,73,964,513) x common factors =1 x 4 = 4
LCM(40,73,964,513) = ( 40 × 73 × 964 × 513 ) / 4
LCM(40,73,964,513) = 1444033440 / 4
LCM(40,73,964,513) = 361008360
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FAQs on GCF of Fractions of 8/40, 32/73, 84/964, 970/513
1. What is the HCF of 8,32,84,970?
The HCF of 8,32,84,970 is 2
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 8/40, 32/73, 84/964, 970/513?
Answer: GCF of Numerators as per given numbers 8/40, 32/73, 84/964, 970/513 is
GCF of Numerators i.e. for 8,32,84,970 is 2
LCM of denominators i.e. for 40,73,964,513 is 361008360.
Thus, GCF of Fractions is 2/361008360.Finally, GCF of Fractions for 8/40, 32/73, 84/964, 970/513 is 2/361008360.