## Wednesday, 16 January 2013

### Pondering over Primes (3)

A number's prime factorisation is
23 X 32 X 52
Is the number even or odd? Explain your reasoning.
Name four other factors of this number, other than 2, 3 and 5.

1. since 2 is an even number, 2 to the power of any other number would be an even number as well.

a negative number to the power of a positive number is always a positive number so 3^2 x 5^2 is a positive number.

since a positive x a positive = positive, 2^3 x 3^2 x 5^2 is an even number.

four other factors :
450
300
900
360

2. 2 is an even number so when a number is multiplied by2, the answer will be an even number and the other factors are 600,300, 900 and 360

3. Even. As 2 is a even number, any numbers multiplied by 2 will also be a even number so 2^3 is a even number. Any numbers multiplied by an even number will also give an even number so the answer is a even number. 4 other factors are 6, 10, 15 and 4

4. The number is even. 2multiplied by 2 or more 2's is always an even number and also any number. An even number multiplied by an odd number and the answer is always a even number. Thus, the answer is even.

The four other factors of this numbers are 4, 6, 8, 10

5. The number will be even. Whatever multiplied by 2 will be a even number.

The 4 other factors are 4,6,8 ad 10

6. The number is even as it is multiplied by a multiple of 2 so it will be even.
4 other factors are 8, 9, 4 and 10

7. The number is even as the index is 2 which is a even.any number multiplied by two becomes even or vice-versa
some other factors are 8,4,10,6