Highest common factor-H.C.F
Calculation of H.C.F. 15, 25.50 and 100
A) Regular method ( method of prime factors)
Rule: break the given number into prime factors and then find the product of the prime factors common to the numbers. The product will be the required H.C.F
Thus,
15=5x3
25=5x5
50=2x5x5
100=2x2x5x5
The factor common to all the numbers is 5, hence 5 is the H.C.F of 15, 25,50and 100.
B) Short cut method
1) Take the smallest of the given set numbers (here, 15).
2) Check whether it exactly divides other numbers, if yes, it is the answer – the H.C.F.
3) If no, factories only this number to its prime factors (here15= 5x3x1). Check whether any of these factors9excluding, of course, 1) exactly divides all other numbers in the set. (Here, 5 can exactly divide all other numbers; 25, 50 and 100).
4) Multiply all the prime factors obtained in step (3) above to get the H.C.F (here, the only prime factor obtained is 5 and hence, 5 is the H.C.F) if no prime factor exists as a common factor, the answer is 1. (Since `1’ though not a prime number, is common to all).
C) By division method
1) We divide the greater number by the smaller and find the remainder.
2) Then divide the first divisor by the remainder and find the second remainder.
3) Then divide the second divisor by the second remainder.
4) We repeat this process till remainder is left. This divisor is our required result.
Example: find H.C.F of 34444 and 3556
3444) 3556(1
3444
_____
112) 3444(30
3360
____
84) 112(1
84
___
28) 84(3
84
____
X
Therefore, H.C.F =28
Highest common factor-H.C.F
Highest common factor: the highest common factor of two or more numbers is the greatest numbers is the greatest number which divides each of the exactly. Thus 9 is the highest common factor of 18 and 27. The H.C.F is also called as greatest common measure (G.C.M) and highest common divisor (H.C.D).
For any two positive numbers A and B, we have
A. x B = (L.C.M of A and B) x (H.C.F of A and B).
If only the L.C.M and the H.C.F.’s of two positive numbers are give, we can determine all possible pairs of the two numbers which satisfy the criteria of L.C.M and H.C.F. (given). An example to illustrate this is given later.
The formulae to determine L.C.M and H.C.F of fractions are given as
L.C.M of the numerator numbers
L.C.M of fractions = _____________________________
H.C.M of the denominator numbers
And
H.C.F of the numerator numbers
H.C.F of fractions = _____________________________
L.C.M of the denominator numbers
Provide that the given fractions are first converted into their `` basic’’ form. A 1 basic’ form means that there should be no common factor in the numerator and denominator of a given fraction.
15 3
Thus, a fraction, say ___ when expressed in its ``basic’’ form; yields ___
20 4
Calculation of L.C.M of 3, 4 and 6
Regular method (the method of prime factors)
Resolve the given numbers into their prime factors and then find the product of the highest powers of all the factors that occur in the given numbers. This product will be the required L.C.M
3 = 3 = 3
2
4 = 2 x 2 = 2
6 = 2 x 3 = 2 x 3
Like it on Facebook, Tweet it or share this article on other bookmarking websites.