GCF of 168/70, 420/78, 480/98
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 168/70, 420/78, 480/98 i.e 12/19110 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/70, 420/78, 480/98.
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 168/70,420/78,480/98?
Given fractions are 168/70,420/78,480/98
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 168/70,420/78,480/98, numerators are 168,420,480
Denominators are 70,78,98
The GCF of 168,420,480 is 12 .
LCM of 70,78,98 is 19110.
The greatest common factor of 168/70,420/78,480/98 = [GCF of 168,420,480]/[LCM of 70,78,98]= 12/19110
Therefore, the GCF of 168/70,420/78,480/98 is 12/19110.
To find the highest common factor of 168,420,480, we have to find the factors of both numbers and list the highest common factor.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
The HCF of 168,420,480 is 12.
Lets's calculate GCF of 168,420,480
| 2 | 168, 420, 480 |
| 2 | 84, 210, 240 |
| 3 | 42, 105, 120 |
| 14, 35, 40 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 168,420,480 By Matching Biggest Common Factor Method
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Now, list down the factors of 480
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480
Greatest Common Factor
We found the factors 168,420,480 . The biggest common factor number is the GCF number.
So the greatest common factor 168,420,480 is 12.
Lets's calculate LCM of 70,78,98
| 2 | 70, 78, 98 |
| 7 | 35, 39, 49 |
| 5, 39, 7 |
∴ So the LCM of the given numbers is 2 x 7 x 5 x 39 x 7 = 19110
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/19110
Therefore, the GCF of Fractions 168/70,420/78,480/98 is 12/19110
Least Common Multiple of 70,78,98 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 70,78,98 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,78,98) = 2
common factors(in case of two or more numbers have common factors) = 14
GCF(70,78,98) x common factors =2 x 14 = 28
LCM(70,78,98) = ( 70 × 78 × 98 ) / 28
LCM(70,78,98) = 535080 / 28
LCM(70,78,98) = 19110
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FAQs on GCF of Fractions of 168/70, 420/78, 480/98
1. What is the HCF of 168,420,480?
The HCF of 168,420,480 is 12
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 168/70, 420/78, 480/98?
Answer: GCF of Numerators as per given numbers 168/70, 420/78, 480/98 is
GCF of Numerators i.e. for 168,420,480 is 12
LCM of denominators i.e. for 70,78,98 is 19110.
Thus, GCF of Fractions is 12/19110.Finally, GCF of Fractions for 168/70, 420/78, 480/98 is 12/19110.