Factors of 17
In mathematical terms, factoring or factorization of a number involves writing that number as a product of many other numbers. These factors are usually simpler and smaller objects of the same kind. In other words, factorization is the mathematical decomposition of a specific number.
For example, when we factorize the number 15, we get 3 * 5. Here, we will learn all about what are the factors of 17 and look into some of the properties of the factors of 17. But before that, let us touch upon some basics.
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What are Factors
Factors are those whole numbers (0, 1, 2, 3, ….) that divide the given number exactly and completely without leaving any remainder.
What are Prime Numbers
Numbers that have only two factors, one of them includes the number itself, and the other one is number 1, are prime numbers. Some of the prime numbers are 5, 7, 2, 11, etc.
What are Composite Numbers
They are in contrast to prime numbers in the sense they have more than 2 factors. Whole numbers that are divisible by more than 2 numbers are composite numbers, for example, 18 = 2 * 3 * 3
What are the Factors of 17
From the above definitions, 17 is a prime number. To prove that 17 is a prime number, it should be divisible by at least one prime number which is less than or equal to √17 ≈ 4.12. But 17 cannot be divided evenly by either 2 or 3 hence we infer that it is a prime number.
Finding Positive Factors of 17
To find all the factors of 17, we need to divide 17 by all the whole numbers starting from 1 up to 17, which can give us an even quotient. When we do that we find out: 17/1 = 17 (as it gives a remainder of 0) and 17//7 = 1 (Here also the remainder is 0). So all the divisors of these equations are the factors of 17 which are 1 and 17 (Positive factors of 17)
Finding Negative Factors of 17
All the positive factors of 17 can be converted into its negative factors. Hens the list of negative factors of 17 is -1 and -17.
How Many Factors Does 17 Have
Since we just saw that 17 has two positive factors and two negative factors hence 17 has a total of 4 factors.
Are the Factors of 17 Prime or Composite?
In number theory, we define prime factors of a positive integer as the numbers that exactly divide the integer. This is given by representing 17 due to the product of prime numbers hence the prime factorization of 17 is 17. 17 is not a composite number as none of the two factors of 17 (1 and 17) is the same number.
Factor Pairs of 17
Factor pairs of a number are two numbers which when multiplied with each other give that number as a result.
1 * 17 = 17 and 17 * 1 = 17 hence pair factors of 17 are (1, 17) and (17, 1)
-1 * -17 = 17 and -17 * -1 = 17 hence pair factors of 17 are (-1, -17) and (-17,-1)
Properties of Factors
Below are a few important properties of factors:
Every whole number can be expressed as the product of number 1 and itself, i.e. each number is a factor of itself.
1 is the factor of every number, i.e. all numbers are divisible by 1.
Every number is a factor of 0, i.e. all numbers when multiplied with 0 give 0 as a result.
The smallest factor of a multiple is 1, and the greatest factor of a multiple is the multiple itself.
All numbers (except 1) have at least 2 factors which are the number 1 and itself.