GCF of 5040/965, 9744/1458
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5040/965, 9744/1458 i.e 336/1406970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5040/965, 9744/1458.
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 5040/965,9744/1458?
Given fractions are 5040/965,9744/1458
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 5040/965,9744/1458, numerators are 5040,9744
Denominators are 965,1458
The GCF of 5040,9744 is 336 .
LCM of 965,1458 is 1406970.
The greatest common factor of 5040/965,9744/1458 = [GCF of 5040,9744]/[LCM of 965,1458]= 336/1406970
Therefore, the GCF of 5040/965,9744/1458 is 336/1406970.
To find the highest common factor of 5040,9744, we have to find the factors of both numbers and list the highest common factor.
The factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040
The factors of 9744 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 42, 48, 56, 58, 84, 87, 112, 116, 168, 174, 203, 232, 336, 348, 406, 464, 609, 696, 812, 1218, 1392, 1624, 2436, 3248, 4872, 9744
The HCF of 5040,9744 is 336.
Lets's calculate GCF of 5040,9744
| 2 | 5040, 9744 |
| 2 | 2520, 4872 |
| 2 | 1260, 2436 |
| 2 | 630, 1218 |
| 3 | 315, 609 |
| 7 | 105, 203 |
| 15, 29 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 x 7 = 336
Greatest Common Factor of 5040,9744 By Matching Biggest Common Factor Method
Now, list down the factors of 5040
:1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,28,30,35,36,40,42,45,48,56,60,63,70,72,80,84,90,105,112,120,126,140,144,168,180,210,240,252,280,315,336,360,420,504,560,630,720,840,1008,1260,1680,2520,5040
Now, list down the factors of 9744
:1,2,3,4,6,7,8,12,14,16,21,24,28,29,42,48,56,58,84,87,112,116,168,174,203,232,336,348,406,464,609,696,812,1218,1392,1624,2436,3248,4872,9744
Greatest Common Factor
We found the factors 5040,9744 . The biggest common factor number is the GCF number.
So the greatest common factor 5040,9744 is 336.
Lets's calculate LCM of 965,1458
Given numbers has no common factors except 1. So, there LCM is their product i.e 1406970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 336/1406970
Therefore, the GCF of Fractions 5040/965,9744/1458 is 336/1406970
Least Common Multiple of 965,1458 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 965,1458 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(965,1458) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(965,1458) x common factors =1 x 1 = 1
LCM(965,1458) = ( 965 × 1458 ) / 1
LCM(965,1458) = 1406970 / 1
LCM(965,1458) = 1406970
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FAQs on GCF of Fractions of 5040/965, 9744/1458
1. What is the HCF of 5040,9744?
The HCF of 5040,9744 is 336
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 5040/965, 9744/1458?
Answer: GCF of Numerators as per given numbers 5040/965, 9744/1458 is
GCF of Numerators i.e. for 5040,9744 is 336
LCM of denominators i.e. for 965,1458 is 1406970.
Thus, GCF of Fractions is 336/1406970.Finally, GCF of Fractions for 5040/965, 9744/1458 is 336/1406970.