High Factors?

Question

Can anyone tell me what number between 1 and 100 with the most factors, and can anyone tell me how you work out a factor.

Answer 1

Since smaller factors give smaller numbers, the basic approach is to multiply small factors together until your result goes over 100. That being said, there are several interpretations of your question.


If you mean non-unique prime factors, the answer would be either 64 (2*2*2*2*2*2) or 96 (2*2*2*2*2*3).

If you mean unique prime factors, the answer is 30 (2*3*5).

If you mean general factors, the answer is either 96 (2*2*2*2*2*3), which has 12 factors (1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96), or 72 (2*2*2*3*3), which also has 12 factors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72).

Answer 2

A factor of an integer is an integer that divides into it with no remainder.

The answer to your question is probably either 90, 96, or 72.

You'll see why if you start listing all the factors.

In general, an integer can be written as product of prime numbers, each raised to a power. For example, 90 is 2^1 * 3^2 * 5^1. Not coincidentally, the number of factors it has is (1+1) * (2+1) * (1+1) = 12.

The

Answer 3

To find a factor.
Divide the number by the prime numbers starting with 2.
If 2 doesn't then use 3 and so on.
The number of denominators use are the factors
e.g.
2) 100
2) 50
5) 25
5) 5
= 1
So 2 and 5 are factors of 100.
also any combination of 2,2,5 & 5 are also factors of 100.

Answer 4

Numbers with a lot of factors tend to have many small factors.

60, for example has 2, 2, 3, 5, plus all the combinations of those

I think 96 might have more 2, 2, 2, 2, 2, 3

Within the set of integers, x factors z if and only if there exists a integer y such that xy = z.

Answer 5

Steve gives a very good answer.