GCF of 1654/649, 8352/213
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1654/649, 8352/213 i.e 2/138237 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1654/649, 8352/213.
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 1654/649,8352/213?
Given fractions are 1654/649,8352/213
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 1654/649,8352/213, numerators are 1654,8352
Denominators are 649,213
The GCF of 1654,8352 is 2 .
LCM of 649,213 is 138237.
The greatest common factor of 1654/649,8352/213 = [GCF of 1654,8352]/[LCM of 649,213]= 2/138237
Therefore, the GCF of 1654/649,8352/213 is 2/138237.
To find the highest common factor of 1654,8352, we have to find the factors of both numbers and list the highest common factor.
The factors of 1654 are 1, 2, 827, 1654
The factors of 8352 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 29, 32, 36, 48, 58, 72, 87, 96, 116, 144, 174, 232, 261, 288, 348, 464, 522, 696, 928, 1044, 1392, 2088, 2784, 4176, 8352
The HCF of 1654,8352 is 2.
Lets's calculate GCF of 1654,8352
| 2 | 1654, 8352 |
| 827, 4176 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1654,8352 By Matching Biggest Common Factor Method
Now, list down the factors of 1654
:1,2,827,1654
Now, list down the factors of 8352
:1,2,3,4,6,8,9,12,16,18,24,29,32,36,48,58,72,87,96,116,144,174,232,261,288,348,464,522,696,928,1044,1392,2088,2784,4176,8352
Greatest Common Factor
We found the factors 1654,8352 . The biggest common factor number is the GCF number.
So the greatest common factor 1654,8352 is 2.
Lets's calculate LCM of 649,213
Given numbers has no common factors except 1. So, there LCM is their product i.e 138237
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/138237
Therefore, the GCF of Fractions 1654/649,8352/213 is 2/138237
Least Common Multiple of 649,213 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 649,213 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(649,213) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(649,213) x common factors =1 x 1 = 1
LCM(649,213) = ( 649 × 213 ) / 1
LCM(649,213) = 138237 / 1
LCM(649,213) = 138237
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FAQs on GCF of Fractions of 1654/649, 8352/213
1. What is the HCF of 1654,8352?
The HCF of 1654,8352 is 2
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 1654/649, 8352/213?
Answer: GCF of Numerators as per given numbers 1654/649, 8352/213 is
GCF of Numerators i.e. for 1654,8352 is 2
LCM of denominators i.e. for 649,213 is 138237.
Thus, GCF of Fractions is 2/138237.Finally, GCF of Fractions for 1654/649, 8352/213 is 2/138237.