GCF of 1872/160, 6840/9706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1872/160, 6840/9706 i.e 72/776480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1872/160, 6840/9706.
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 1872/160,6840/9706?
Given fractions are 1872/160,6840/9706
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 1872/160,6840/9706, numerators are 1872,6840
Denominators are 160,9706
The GCF of 1872,6840 is 72 .
LCM of 160,9706 is 776480.
The greatest common factor of 1872/160,6840/9706 = [GCF of 1872,6840]/[LCM of 160,9706]= 72/776480
Therefore, the GCF of 1872/160,6840/9706 is 72/776480.
To find the highest common factor of 1872,6840, we have to find the factors of both numbers and list the highest common factor.
The factors of 1872 are 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 48, 52, 72, 78, 104, 117, 144, 156, 208, 234, 312, 468, 624, 936, 1872
The factors of 6840 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 30, 36, 38, 40, 45, 57, 60, 72, 76, 90, 95, 114, 120, 152, 171, 180, 190, 228, 285, 342, 360, 380, 456, 570, 684, 760, 855, 1140, 1368, 1710, 2280, 3420, 6840
The HCF of 1872,6840 is 72.
Lets's calculate GCF of 1872,6840
| 2 | 1872, 6840 |
| 2 | 936, 3420 |
| 2 | 468, 1710 |
| 3 | 234, 855 |
| 3 | 78, 285 |
| 26, 95 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 3 = 72
Greatest Common Factor of 1872,6840 By Matching Biggest Common Factor Method
Now, list down the factors of 1872
:1,2,3,4,6,8,9,12,13,16,18,24,26,36,39,48,52,72,78,104,117,144,156,208,234,312,468,624,936,1872
Now, list down the factors of 6840
:1,2,3,4,5,6,8,9,10,12,15,18,19,20,24,30,36,38,40,45,57,60,72,76,90,95,114,120,152,171,180,190,228,285,342,360,380,456,570,684,760,855,1140,1368,1710,2280,3420,6840
Greatest Common Factor
We found the factors 1872,6840 . The biggest common factor number is the GCF number.
So the greatest common factor 1872,6840 is 72.
Lets's calculate LCM of 160,9706
| 2 | 160, 9706 |
| 80, 4853 |
∴ So the LCM of the given numbers is 2 x 80 x 4853 = 776480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 72/776480
Therefore, the GCF of Fractions 1872/160,6840/9706 is 72/776480
Least Common Multiple of 160,9706 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 160,9706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(160,9706) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(160,9706) x common factors =2 x 1 = 2
LCM(160,9706) = ( 160 × 9706 ) / 2
LCM(160,9706) = 1552960 / 2
LCM(160,9706) = 776480
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FAQs on GCF of Fractions of 1872/160, 6840/9706
1. What is the HCF of 1872,6840?
The HCF of 1872,6840 is 72
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 1872/160, 6840/9706?
Answer: GCF of Numerators as per given numbers 1872/160, 6840/9706 is
GCF of Numerators i.e. for 1872,6840 is 72
LCM of denominators i.e. for 160,9706 is 776480.
Thus, GCF of Fractions is 72/776480.Finally, GCF of Fractions for 1872/160, 6840/9706 is 72/776480.