why does 16 have an odd number of factors Square numbers are formed by multiplying a number by itself such as 9 16 25 All square numbers have an odd number of factors Let s take some examples Factors of 9 1
Note that 100 has an odd number of factors which means that is a perfect square The prime factors of 100 are 2 and 5 and the highest powers of these contained in 100 are 4 Specifically looking at the factors of 16 there are some interesting properties 16 is a square number which means that it has an odd number of factors
why does 16 have an odd number of factors
why does 16 have an odd number of factors
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A factor is a number that divides into another number exactly and without leaving a remainder Most numbers have an even number of factors however a square The short answer to your question is that they don t Only the numbers that are perfect squares have an odd number of factors For example the factors of 16 are 1 2 4 8 16
Perfect squares also called square numbers have an odd number of factors and primes squared have 3 factors Brief Explanation If you start with a Prime The point is that if k is a factor of n then there is an integer m so that n kxm This adds two to the list of factors m and k unless k m Thus the number of factors is even
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16 also has odd number of factors 1 2 4 8 16 The reason for this is for numbers other than perfect squares all factors are in the form of pairs but for perfect What is the smallest number with exactly 100 factors Which number less than 1000 has the most factors You may be interested in the other problems in our Hidden Treasures
Why do the numbers 16 36 48 60 64 90 and 100 have an odd number of factors Answered by Stephen La Rocque and Penny Nom Odd numbers are numbers that are not divisible by 2 Odd numbers have 1 3 5 7 or 9 at ones place Learn the definition related math activities facts and more
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why does 16 have an odd number of factors - The point is that if k is a factor of n then there is an integer m so that n kxm This adds two to the list of factors m and k unless k m Thus the number of factors is even