Is there an easier way to work this maths question out?
How many numbers are there between 1 and 130 (including 1 and 130) that have an odd number of factors?
It's only worth 3 marks, but all I can figure is to go through every number between 1 and 130 and working out the factors of each, so that's about 10 minutes work, minimum, so I can't see that only being worth 3 marks, so is there a shortcut or formula that simplifies this task??
2006-10-01 04:39:55 · 7 answers · asked by Anonymous in Education & Reference ➔ Homework Help
There is a very easy way. Any number (apart from special ones) has even factors. This is because to have a factor, it has to be divided by x to make y. So, for example, 12 has the factors 1 and 12, 2 and 6, 3 and 4. Each one comes in pairs, making an even number of factors.
The next question is what can make it a special one. The answer is when the same number appears twice in the factor. i.e. 4 has the factors 1*4 and 2*2, so its list of factors is 1,2,4 which is an odd number. So all square numbers have an odd number of factors. So all you have to do is find all the square numbers from 1 to 130.
(NB Think about cube numbers and ^4 numbers as well. They don't count, but you might want to investigate them to find out why).
Your final answer is therefore going to be 1,4,9,16... up to 121 (which is 11*11)
2006-10-01 04:59:32 · answer #1 · answered by Steve-Bob 4 · 1⤊ 0⤋
There are only 11 numbers. Only squared numbers will have an odd number of factors. Think of it: Factors come in pairs, but if the number is squared, the two factors are the same, thus are counted as one. For example, factors of 16: 1, 16, 2, 8, 4 (16 is 4^2).
2006-10-01 11:49:02 · answer #2 · answered by chingmenghang 3 · 3⤊ 0⤋
I may be wrong, but I don't think any number has an odd number of factors, even if you reduce them to prime numbers. All prime numbers have only 2 factors. 10 has 4 factors, 5, 2, 1, and 10. 12 has 1, 12, 2, 6, 3, and 4. 25 has 5, 5, 1, 25. Do you count factors that are the same, like in squared numbers? Otherwise, like I said, I don't think any number has an odd number of them.
2006-10-01 11:50:07 · answer #3 · answered by poohmanchu3 2 · 0⤊ 3⤋
Look for the square numbers they have an odd number of factors
2006-10-03 16:32:15 · answer #4 · answered by JuJu 3 · 0⤊ 0⤋
I think you just have to figure it out! It's standard maths to know the factors, so you just have to do it the tedious way and make a list! That's the only way I know - sorry!
2006-10-01 11:48:50 · answer #5 · answered by sammi 6 · 0⤊ 2⤋
Not even a calculator can help there! And nether can I, sorry. Any way, why would anyone want to know the answer to that?
2006-10-01 11:53:16 · answer #6 · answered by Dean P 2 · 0⤊ 2⤋
there isn't a shorter way to my knoeledge, try a site called www.mathformorons.com. it has loads of maths tips.
2006-10-01 11:43:53 · answer #7 · answered by bxiok 2 · 0⤊ 2⤋