Factors of 17 | Prime Factorization of 17 - Explained Simply

Today we are going to present here Factor Tree of 17. The factor is the number that divides the original number. The factors of 17 are 1 and 17 itself.

What are the factors of 17?

The factors of 17 are all the whole numbers that, when divided into 17, result in a whole number with no remainder. We can also think of them as the whole numbers that multiply together to give 17.

Factor Tree Method of 17: Explained Simply

Now, let's apply our understanding of factors specifically to the number 17. We will systematically check numbers to see if they divide 17 evenly.

Start with 1:

Can 1 divide 17 evenly? Yes, 17 ÷ 1 = 17. (1 divided by 17 long division.)

So, 1 is a factor of 17. (And based on our rules, 17 is also a factor because it's 17 divided by 1).

Current Factors: {1, 17}

Try 2:

Can 2 divide 17 evenly? 17 ÷ 2 = 8 with a remainder of 1.

No, 2 is not a factor of 17.

Try 3:

Can 3 divide 17 evenly? 17 ÷ 3 = 5 with a remainder of 2.

No, 3 is not a factor of 17.

Try 4:

Can 4 divide 17 evenly? 17 ÷ 4 = 4 with a remainder of 1.

No, 4 is not a factor of 17.

Stopping Point: A useful trick is that you only need to check numbers up to the square root of the number you are factoring. The square root of 17 is approximately 4.12. This means we only need to check whole numbers up to 4. Since we've checked 1, 2, 3, and 4 and haven't found any new factors beyond 1 and 17, we can stop.

Conclusion:

After checking all possible whole numbers up to its square root, we find that the only numbers that divide 17 evenly are 1 and 17.

Prime Factorization of 17

Now, let's apply our understanding to the number 17. Is it prime or composite?

Start checking for divisibility by small prime numbers:

Can 17 divided by 2?

No, 17/2 = 8.5 (not a whole number).

Can 17 be divided evenly by 3?

No, 17/3 = 5.66...

Can 17 be divided evenly by 5?

No, 17/5 = 3.4

Can 17 divided by 7?

No, 17/7 = 2.42...

Rule of thumb: To check if a number n is prime, you only need to test for prime divisors up to the square root of n. The square root of 17 is approximately 4.12. So, we only needed to check prime numbers up to 3 (which are 2 and 3). Since neither 2 nor 3 divide 17 evenly, 17 must be prime.

Recall the definition of a prime number, "A prime number is a natural number greater than 1 that has only two positive divisors 1 and itself."

The only numbers that divide 17 evenly are 1 and 17.

Conclusion:

Based on the definition and our tests, 17 is a prime number.

What is the Prime Factorization of 17?

Since 17 is already a prime number, its prime factorization is simply the number itself.

Prime Factorization of 17 = 17

Think of it this way, 17 is one of those fundamental building blocks that cannot be broken down any further into other prime numbers. It is its own prime factor.