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# Ratio of square numbers to numbers with 4 factors?

Updated: 4/27/2022

Wiki User

16y ago

As N approaches infinity the ratio of squares less than N to numbers with 4 factors less than N approaches 0. This means that in the customary way of defining it, the ratio you're interested in is 0 (although that should be taken with a grain of salt - it certainly doesn't mean that there are 0 square numbers). The number of squares less than N is approximately √N. Rather than calculating the ratio we're interested in, we're going to calculate a calculate a ratio guaranteed to be greater: the ratio of squares to numbers that are twice a Prime number (which are some, but not all, of the numbers with 4 factors). There are approximately N/ln N prime numbers less than N, by the prime number theorem. So there are N/(2 ln N/2) prime numbers less than N/2, which can be doubled to get a number less than N that's twice a prime number. The ratio is therefore √N(2 ln N/2)/N, which is O(ln N/√N). √N grows much faster than ln N, and in the limit this ratio will get close to zero. So the ratio we're actually interested in, which is even less than this ratio, will also approach zero.

Wiki User

16y ago

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Q: Ratio of square numbers to numbers with 4 factors?
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Related questions

### How many square numbers are factors of 1600?

There are two square numbers that are factors of 1600 : 16=4*4 100=10*10.

### What types of numbers has an odd number of factors give examples?

Square numbers have odd numbers of factors.

### Are square numbers factors?

They can be. 4 is a factor of 16.

### Factors of 72 which are square numbers?

They are: 1 4 9 and 36

### What are two examples of a type of number that has an odd number factor?

There are square numbers (numbers which are a square of an integer), such as 4. It's factors, listed are 1, 2, and 4. All square numbers have an odd number of factors. Then there's 1, which has only 1 factor: 1. All other numbers have an even number of factors. Prime numbers will have only 2 factors (2 is even).

### What type of number has an odd number of factors example?

Square numbers have odd numbers of factors. Examples: 4, 9, 16

### A square number that is a factor of 100?

Both 25 and 4 are factors of 100 and are square numbers, 25 is 52 and 4 is 22. 100 and 1 are also factors of 100, and are also square numbers: 1 is 12 and 100 is 102.

### Do all square numbers have exactly 3 factors?

No. 81=9*9=3*27=1*81 81 has 5 factors and is a square number. 36=6*6=3*12=1*36=2*18=4*9 36 has 9 factors and is a square number. This doesn't mean that no square numbers have exactly 3 factors though, because: 9=3*3=1*9 9 has 3 factors and is a square number. 4=2*2=1*4 4 has 3 factors and is a square number. All square numbers have an odd number of factors though (because they have a whole number which multiplies by itself to get the number). Factors are whole numbers only, and not decimals. Hope this helps :)

### What are four numbers that have an odd amount of factors what do they have in common?

4, 9, 16 and 25 are square numbers.

### What 4 numbers have 3 factors?

Any prime square like, 4, 9, 25 and 49.

### What are the factors of 84 and 105 that are square numbers?

4 is the only square number that is a factor of 84. No square number is a factor of 105.

### What is a number less than 20 and has 3 factors?

4 and 9. Factors of numbers come in pairs which means that every number ought to have an even number of factors. To have an odd number of factors, one factor pair must be a repeated number which means that only square numbers have an odd number of factors. The square numbers less than 20 are 1, 4, 9 &amp; 16 and of these 4 &amp; 9 have 3 factors: 4: 1, 2 &amp; 4 9: 1, 3 &amp; 9