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Perfect Numbers I

A factor of a number is an exact divisor of that number. Now in other words we can say , a factor of a number is the number which completely divides the given number without any remainder. Let us take some examples to understand factors.
Let us factor a number 12, factor of 12 are 1,2,3,4,6 and 12. However, none of the numbers 5,7,8,9,10 and 11 is a factor of 12.Now what are Perfect numbers? if the sum of all the factors of a number is two times the number, then the number is called Perfect number. The factors of 6 are 1,2,3 and 6.Also, 1+2+3+6=12=2*6 i.e sum of all factors of 6 = 2*6 so, 6 is a perfect number. Now let us see if 28 is the perfect number .The factors of 28 are 1,2,4,7,14 and 28.Sum of all factors of 28 = 1+2+4+7+14+28=56+2*28 So,28 is also a perfect number. Note that 12 is not a perfect number.
Procedure for finding factors
Step 1 Obtain the number whose factors are to be listed.
Step2 Divide the number by 2.If the number is divisible by 2, find the quotient and list 2 and other factor (quotient) just below 2.
Step3 Divide the number by 3.If the number is divisible ...
... by 3, find the quotient and list 3 and the quotient just below 3.
Step4 Divide the number by 4.If the number is divisible by 4, find the quotient and list 4 and the quotient just below 4
Continue this process with 5,6,7 etc. till you get a factor which has already been listed.
Let us take some example of factor, Find factors of a numbers 24:-
(a) 24 The given number is 24. Clearly, 1 and 24 are its factors. So, we list 1 and 24.We find that if we divide 24 by 2, the quotient is 12 and the remainder is zero. Therefore, 24 is divisible by 2. S, we list 2 and 12.When 24 is divided by 3, the quotient is 8 and the remainder is zero.
So,24 is divisible by 3 and we list 3 and 8.Now, we divide 24 by 4. Clearly, when we divide 24 by 4, we obtain 6 as the quotient and the remainder as zero. So, 24 is also divisible by 4 and we list 4 and 6.Clearly,24 is not divisible by 5. The next number is 6, which has already been listed as a factor.
So, we stop the procedure and list the
factors of 24 as given below:
1 2 3 4
24 12 8 6
(b) The given number is 64.To factor a number clearly; it is divisible by 1,2,4,8 etc. So, its factors or Factor Numbers are as listed below.1 2 4 8 64 32 16 8
(c) The given number is 144. Clearly ,it is divisible by 1,2,4,6,8,12,16,24,etc.So,factors of 144 are:1 2 3 4 6 8 9 12 144 72 48 36 24 18 16 12
Know more about the Exponential Function Definition, online tutoring,Properties Of Exponential Functions. Online tutoring will help us to learn and do our homework very easily without going here and there.
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