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Chapter 1: Problem 34

Find all integer factors of each number. $$ 17 $$

Short Answer

Expert verified
The integer factors of 17 are 1 and 17.

Step by step solution

01

- Understand the Problem

The problem asks to find all integer factors of the number 17. An integer factor of a number is a whole number that can be multiplied by another whole number to produce the original number.
02

- Identify and Test Potential Factors

Start testing potential factors starting from 1 up to the number itself. For 17, test the divisibility by 1 and 17, as these are always factors of any integer number.
03

- Check Divisibility

Check if 17 can be divided by integers between 2 and 16 without leaving a remainder. Since 17 is a prime number, it cannot be divided evenly by any other number apart from 1 and 17.
04

- List All Factors

Since 17 is a prime number, its only integer factors are 1 and 17.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

integer factors
Integer factors of a number are whole numbers that you can multiply together to get the original number. For example, if you multiply 2 by 3, you get 6, so 2 and 3 are factors of 6.
When finding factors, start with the number 1 and the given number itself because these are always factors.
Next, test other smaller numbers to see if they divide evenly into the given number without leaving a remainder.
For instance, to find the factors of 17, you see if 17 can be divided evenly by numbers between 1 and 17.
If no whole number other than 1 and 17 divides it without leaving a remainder, then 17 is prime.
In summary, 17鈥檚 only integer factors are 1 and 17.
prime numbers
Prime numbers are numbers greater than 1 that only have two factors: 1 and themselves.
For example, 2, 3, 5, 11, and 17 are all prime numbers because they can't be divided evenly by any other numbers.
To determine if a number is prime, test its divisibility by all numbers up to its square root.
If none of these numbers divide evenly, then the number is prime.
Prime numbers are useful in many areas of mathematics and are the building blocks of whole numbers because every number can be expressed as a product of prime numbers (prime factorization).
For instance, 6 can be written as 2 脳 3, both of which are primes.
divisibility
Divisibility means determining whether one number can be divided by another without leaving a remainder.
For example, 10 is divisible by 2 because dividing 10 by 2 equals 5, with no remainder.
To check if a number is divisible by another, remember some simple rules:
  • A number is divisible by 2 if it is even (ends in 0, 2, 4, 6, or 8).
  • A number is divisible by 3 if the sum of its digits is divisible by 3.
  • A number is divisible by 5 if it ends in 0 or 5.
Using these rules, you can quickly determine if a number divides another number evenly.
For 17, since it doesn't meet any basic divisibility rules for numbers other than 1 and itself, it's confirmed as a prime number.

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Most popular questions from this chapter

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 2 if its last digit is divisible by \(2,\) and not otherwise. Show that (a) \(3,473,986\) is divisible by 2 and (b) \(4,336,879\) is not divisible by 2 .

Simplify each expression. $$ -4(-3 x+3)-(6 x-4)-2 x+1 $$

Simplify each expression. $$ -9 m^{3}+3 m^{3}-7 m^{3} $$

Simplify each expression. $$ -7.5(2 y+4)-2.9(3 y-6) $$

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. A number multiplied by \(5,\) subtracted from the sum of 14 and eight times the number
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