利用質因數分解法,求H.C.F和L.C.H的問題

In order to get the H.C.F,we usually get the same prime factors in 2 or above
number to calculate it.
For example,
30=2x3x5
69=3x23

In this case,factor 3 appear in both side.Therefore the H.C.F of 30 and 69 is 3.
For another example,
210=2x3x5x7
440=2x2x2x5x11
1000=2x2x2x5x5x5

In this case,Factor 2,5 appear in both side.Therefore the H.C.F of 210,440 and
1000 is 2x5=10
(p.s. we usually divide the number from the smallest prime factor first.like 2,3,5,7
do not try to divide the number from large prime numbed in first time.like 23,59.
Although it wastes a lot of time in calculating large number,it is very useful.)
If you try many prime number but still cannot divide it(Let it be X)
And (The prime number you had tried)>√(X), X should be a prime number too.

In order to get the L.C.M.,we should find the different prime factors in 2 or above
number to calculate it.
For example,
39=3x13
27=3x3x3
In this case,we can find the common factor(3)and the different factor(3x3,13)
39 does not have enough 3 so we can times 3x3 on it to make it become
39x3x3=3x3x3x13

27 does not have 13 so we put (x13) in it to make it become
27x13=3x3x3x13

Therefore their L.C.M is 3x3x3x13=351

Now,you should know how to find H.C.F and L.C.M. now!!!

求 12 與 18 的 H.C.F. 和 L.C.M.

12 = 2 x 2 x 3 = 2^2 x 3
18 = 2 x 3 x 3 = 2 x 3^2
H.C.F. = 2 x 3 = 6
L.C.M. = 2^2 x 3^2 = 36

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