GCF of 669/69, 420/117
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 669/69, 420/117 i.e 3/2691 easily. The following is the detailed procedure to determine the greatest common factor of fractions 669/69, 420/117.
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 669/69,420/117?
Given fractions are 669/69,420/117
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 669/69,420/117, numerators are 669,420
Denominators are 69,117
The GCF of 669,420 is 3 .
LCM of 69,117 is 2691.
The greatest common factor of 669/69,420/117 = [GCF of 669,420]/[LCM of 69,117]= 3/2691
Therefore, the GCF of 669/69,420/117 is 3/2691.
To find the highest common factor of 669,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 669 are 1, 3, 223, 669
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 HCF of 669,420 is 3.
Lets's calculate GCF of 669,420
| 3 | 669, 420 |
| 223, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 669,420 By Matching Biggest Common Factor Method
Now, list down the factors of 669
:1,3,223,669
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
Greatest Common Factor
We found the factors 669,420 . The biggest common factor number is the GCF number.
So the greatest common factor 669,420 is 3.
Lets's calculate LCM of 69,117
| 3 | 69, 117 |
| 23, 39 |
∴ So the LCM of the given numbers is 3 x 23 x 39 = 2691
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2691
Therefore, the GCF of Fractions 669/69,420/117 is 3/2691
Least Common Multiple of 69,117 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 69,117 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,117) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,117) x common factors =3 x 1 = 3
LCM(69,117) = ( 69 × 117 ) / 3
LCM(69,117) = 8073 / 3
LCM(69,117) = 2691
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 669/69, 420/117
1. What is the HCF of 669,420?
The HCF of 669,420 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 669/69, 420/117?
Answer: GCF of Numerators as per given numbers 669/69, 420/117 is
GCF of Numerators i.e. for 669,420 is 3
LCM of denominators i.e. for 69,117 is 2691.
Thus, GCF of Fractions is 3/2691.Finally, GCF of Fractions for 669/69, 420/117 is 3/2691.