GCF of 420/112, 9750/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 420/112, 9750/209 i.e 30/23408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/112, 9750/209.
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 420/112,9750/209?
Given fractions are 420/112,9750/209
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 420/112,9750/209, numerators are 420,9750
Denominators are 112,209
The GCF of 420,9750 is 30 .
LCM of 112,209 is 23408.
The greatest common factor of 420/112,9750/209 = [GCF of 420,9750]/[LCM of 112,209]= 30/23408
Therefore, the GCF of 420/112,9750/209 is 30/23408.
To find the highest common factor of 420,9750, we have to find the factors of both numbers and list the highest common factor.
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 9750 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875, 9750
The HCF of 420,9750 is 30.
Lets's calculate GCF of 420,9750
| 2 | 420, 9750 |
| 3 | 210, 4875 |
| 5 | 70, 1625 |
| 14, 325 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 420,9750 By Matching Biggest Common Factor Method
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 9750
:1,2,3,5,6,10,13,15,25,26,30,39,50,65,75,78,125,130,150,195,250,325,375,390,650,750,975,1625,1950,3250,4875,9750
Greatest Common Factor
We found the factors 420,9750 . The biggest common factor number is the GCF number.
So the greatest common factor 420,9750 is 30.
Lets's calculate LCM of 112,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 23408
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/23408
Therefore, the GCF of Fractions 420/112,9750/209 is 30/23408
Least Common Multiple of 112,209 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 112,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(112,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(112,209) x common factors =1 x 1 = 1
LCM(112,209) = ( 112 × 209 ) / 1
LCM(112,209) = 23408 / 1
LCM(112,209) = 23408
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FAQs on GCF of Fractions of 420/112, 9750/209
1. What is the HCF of 420,9750?
The HCF of 420,9750 is 30
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 420/112, 9750/209?
Answer: GCF of Numerators as per given numbers 420/112, 9750/209 is
GCF of Numerators i.e. for 420,9750 is 30
LCM of denominators i.e. for 112,209 is 23408.
Thus, GCF of Fractions is 30/23408.Finally, GCF of Fractions for 420/112, 9750/209 is 30/23408.