GCF of 32/65, 74/76, 84/16, 18/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 32/65, 74/76, 84/16, 18/400 i.e 2/98800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/65, 74/76, 84/16, 18/400.
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 32/65,74/76,84/16,18/400?
Given fractions are 32/65,74/76,84/16,18/400
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 32/65,74/76,84/16,18/400, numerators are 32,74,84,18
Denominators are 65,76,16,400
The GCF of 32,74,84,18 is 2 .
LCM of 65,76,16,400 is 98800.
The greatest common factor of 32/65,74/76,84/16,18/400 = [GCF of 32,74,84,18]/[LCM of 65,76,16,400]= 2/98800
Therefore, the GCF of 32/65,74/76,84/16,18/400 is 2/98800.
To find the highest common factor of 32,74,84,18, we have to find the factors of both numbers and list the highest common factor.
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 74 are 1, 2, 37, 74
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 18 are 1, 2, 3, 6, 9, 18
The HCF of 32,74,84,18 is 2.
Lets's calculate GCF of 32,74,84,18
| 2 | 32, 74, 84, 18 |
| 16, 37, 42, 9 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 32,74,84,18 By Matching Biggest Common Factor Method
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 74
:1,2,37,74
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 18
:1,2,3,6,9,18
Greatest Common Factor
We found the factors 32,74,84,18 . The biggest common factor number is the GCF number.
So the greatest common factor 32,74,84,18 is 2.
Lets's calculate LCM of 65,76,16,400
| 2 | 65, 76, 16, 400 |
| 2 | 65, 38, 8, 200 |
| 2 | 65, 19, 4, 100 |
| 2 | 65, 19, 2, 50 |
| 5 | 65, 19, 1, 25 |
| 13, 19, 1, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 5 x 13 x 19 x 1 x 5 = 98800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/98800
Therefore, the GCF of Fractions 32/65,74/76,84/16,18/400 is 2/98800
Least Common Multiple of 65,76,16,400 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 65,76,16,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,76,16,400) = 1
common factors(in case of two or more numbers have common factors) = 320
GCF(65,76,16,400) x common factors =1 x 320 = 320
LCM(65,76,16,400) = ( 65 × 76 × 16 × 400 ) / 320
LCM(65,76,16,400) = 31616000 / 320
LCM(65,76,16,400) = 98800
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FAQs on GCF of Fractions of 32/65, 74/76, 84/16, 18/400
1. What is the HCF of 32,74,84,18?
The HCF of 32,74,84,18 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 32/65, 74/76, 84/16, 18/400?
Answer: GCF of Numerators as per given numbers 32/65, 74/76, 84/16, 18/400 is
GCF of Numerators i.e. for 32,74,84,18 is 2
LCM of denominators i.e. for 65,76,16,400 is 98800.
Thus, GCF of Fractions is 2/98800.Finally, GCF of Fractions for 32/65, 74/76, 84/16, 18/400 is 2/98800.