GCF of 93/70, 21/61, 840/19
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 93/70, 21/61, 840/19 i.e 3/81130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 93/70, 21/61, 840/19.
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 93/70,21/61,840/19?
Given fractions are 93/70,21/61,840/19
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 93/70,21/61,840/19, numerators are 93,21,840
Denominators are 70,61,19
The GCF of 93,21,840 is 3 .
LCM of 70,61,19 is 81130.
The greatest common factor of 93/70,21/61,840/19 = [GCF of 93,21,840]/[LCM of 70,61,19]= 3/81130
Therefore, the GCF of 93/70,21/61,840/19 is 3/81130.
To find the highest common factor of 93,21,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 93 are 1, 3, 31, 93
The factors of 21 are 1, 3, 7, 21
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 93,21,840 is 3.
Lets's calculate GCF of 93,21,840
| 3 | 93, 21, 840 |
| 31, 7, 280 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 93,21,840 By Matching Biggest Common Factor Method
Now, list down the factors of 93
:1,3,31,93
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 93,21,840 . The biggest common factor number is the GCF number.
So the greatest common factor 93,21,840 is 3.
Lets's calculate LCM of 70,61,19
Given numbers has no common factors except 1. So, there LCM is their product i.e 81130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/81130
Therefore, the GCF of Fractions 93/70,21/61,840/19 is 3/81130
Least Common Multiple of 70,61,19 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 70,61,19 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,61,19) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(70,61,19) x common factors =1 x 1 = 1
LCM(70,61,19) = ( 70 × 61 × 19 ) / 1
LCM(70,61,19) = 81130 / 1
LCM(70,61,19) = 81130
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FAQs on GCF of Fractions of 93/70, 21/61, 840/19
1. What is the HCF of 93,21,840?
The HCF of 93,21,840 is 3
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 93/70, 21/61, 840/19?
Answer: GCF of Numerators as per given numbers 93/70, 21/61, 840/19 is
GCF of Numerators i.e. for 93,21,840 is 3
LCM of denominators i.e. for 70,61,19 is 81130.
Thus, GCF of Fractions is 3/81130.Finally, GCF of Fractions for 93/70, 21/61, 840/19 is 3/81130.