GCF of 690/672, 7222/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 690/672, 7222/749 i.e 46/71904 easily. The following is the detailed procedure to determine the greatest common factor of fractions 690/672, 7222/749.
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 690/672,7222/749?
Given fractions are 690/672,7222/749
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 690/672,7222/749, numerators are 690,7222
Denominators are 672,749
The GCF of 690,7222 is 46 .
LCM of 672,749 is 71904.
The greatest common factor of 690/672,7222/749 = [GCF of 690,7222]/[LCM of 672,749]= 46/71904
Therefore, the GCF of 690/672,7222/749 is 46/71904.
To find the highest common factor of 690,7222, we have to find the factors of both numbers and list the highest common factor.
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The factors of 7222 are 1, 2, 23, 46, 157, 314, 3611, 7222
The HCF of 690,7222 is 46.
Lets's calculate GCF of 690,7222
| 2 | 690, 7222 |
| 23 | 345, 3611 |
| 15, 157 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 690,7222 By Matching Biggest Common Factor Method
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Now, list down the factors of 7222
:1,2,23,46,157,314,3611,7222
Greatest Common Factor
We found the factors 690,7222 . The biggest common factor number is the GCF number.
So the greatest common factor 690,7222 is 46.
Lets's calculate LCM of 672,749
| 7 | 672, 749 |
| 96, 107 |
∴ So the LCM of the given numbers is 7 x 96 x 107 = 71904
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/71904
Therefore, the GCF of Fractions 690/672,7222/749 is 46/71904
Least Common Multiple of 672,749 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 672,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(672,749) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(672,749) x common factors =7 x 1 = 7
LCM(672,749) = ( 672 × 749 ) / 7
LCM(672,749) = 503328 / 7
LCM(672,749) = 71904
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 690/672, 7222/749
1. What is the HCF of 690,7222?
The HCF of 690,7222 is 46
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 690/672, 7222/749?
Answer: GCF of Numerators as per given numbers 690/672, 7222/749 is
GCF of Numerators i.e. for 690,7222 is 46
LCM of denominators i.e. for 672,749 is 71904.
Thus, GCF of Fractions is 46/71904.Finally, GCF of Fractions for 690/672, 7222/749 is 46/71904.