GCF of 869/420, 120/510
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 869/420, 120/510 i.e 1/7140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 869/420, 120/510.
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 869/420,120/510?
Given fractions are 869/420,120/510
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 869/420,120/510, numerators are 869,120
Denominators are 420,510
The GCF of 869,120 is 1 .
LCM of 420,510 is 7140.
The greatest common factor of 869/420,120/510 = [GCF of 869,120]/[LCM of 420,510]= 1/7140
Therefore, the GCF of 869/420,120/510 is 1/7140.
To find the highest common factor of 869,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 869 are 1, 11, 79, 869
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 869,120 is 1.
Lets's calculate GCF of 869,120
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 869,120 By Matching Biggest Common Factor Method
Now, list down the factors of 869
:1,11,79,869
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 869,120 . The biggest common factor number is the GCF number.
So the greatest common factor 869,120 is 1.
Lets's calculate LCM of 420,510
| 2 | 420, 510 |
| 3 | 210, 255 |
| 5 | 70, 85 |
| 14, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 14 x 17 = 7140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7140
Therefore, the GCF of Fractions 869/420,120/510 is 1/7140
Least Common Multiple of 420,510 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 420,510 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,510) = 30
common factors(in case of two or more numbers have common factors) = 1
GCF(420,510) x common factors =30 x 1 = 30
LCM(420,510) = ( 420 × 510 ) / 30
LCM(420,510) = 214200 / 30
LCM(420,510) = 7140
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FAQs on GCF of Fractions of 869/420, 120/510
1. What is the HCF of 869,120?
The HCF of 869,120 is 1
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 869/420, 120/510?
Answer: GCF of Numerators as per given numbers 869/420, 120/510 is
GCF of Numerators i.e. for 869,120 is 1
LCM of denominators i.e. for 420,510 is 7140.
Thus, GCF of Fractions is 1/7140.Finally, GCF of Fractions for 869/420, 120/510 is 1/7140.