GCF of 1470/142, 7819/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1470/142, 7819/420 i.e 7/29820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1470/142, 7819/420.
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 1470/142,7819/420?
Given fractions are 1470/142,7819/420
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 1470/142,7819/420, numerators are 1470,7819
Denominators are 142,420
The GCF of 1470,7819 is 7 .
LCM of 142,420 is 29820.
The greatest common factor of 1470/142,7819/420 = [GCF of 1470,7819]/[LCM of 142,420]= 7/29820
Therefore, the GCF of 1470/142,7819/420 is 7/29820.
To find the highest common factor of 1470,7819, we have to find the factors of both numbers and list the highest common factor.
The factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470
The factors of 7819 are 1, 7, 1117, 7819
The HCF of 1470,7819 is 7.
Lets's calculate GCF of 1470,7819
| 7 | 1470, 7819 |
| 210, 1117 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 1470,7819 By Matching Biggest Common Factor Method
Now, list down the factors of 1470
:1,2,3,5,6,7,10,14,15,21,30,35,42,49,70,98,105,147,210,245,294,490,735,1470
Now, list down the factors of 7819
:1,7,1117,7819
Greatest Common Factor
We found the factors 1470,7819 . The biggest common factor number is the GCF number.
So the greatest common factor 1470,7819 is 7.
Lets's calculate LCM of 142,420
| 2 | 142, 420 |
| 71, 210 |
∴ So the LCM of the given numbers is 2 x 71 x 210 = 29820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/29820
Therefore, the GCF of Fractions 1470/142,7819/420 is 7/29820
Least Common Multiple of 142,420 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 142,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,420) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,420) x common factors =2 x 1 = 2
LCM(142,420) = ( 142 × 420 ) / 2
LCM(142,420) = 59640 / 2
LCM(142,420) = 29820
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FAQs on GCF of Fractions of 1470/142, 7819/420
1. What is the HCF of 1470,7819?
The HCF of 1470,7819 is 7
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 1470/142, 7819/420?
Answer: GCF of Numerators as per given numbers 1470/142, 7819/420 is
GCF of Numerators i.e. for 1470,7819 is 7
LCM of denominators i.e. for 142,420 is 29820.
Thus, GCF of Fractions is 7/29820.Finally, GCF of Fractions for 1470/142, 7819/420 is 7/29820.