Practice Makes Perfect

## Identify Prime and Composite Numbers

Some numbers, like (72), have actually many type of components. Other numbers, such as (7), have actually only two factors: (1) and also the number. A number through just two factors is called a prime number. A number through more than two components is called a composite number. The number (1) is neither prime nor composite. It has just one factor, itself.

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Definition: Prime Numbers and also Composite Numbers

A prime number is a counting number higher than (1) whose just determinants are (1) and itself.

A compowebsite number is a counting number that is not prime.

Figure (PageIndex5) lists the counting numbers from (2) via (20) together with their determinants. The highlighted numbers are prime, considering that each has actually only two determinants.

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HOW TO: DETERMINE IF A NUMBER IS PRIME.

Tip 1. Test each of the primes, in order, to watch if it is a factor of the number. Tip 2. Start with (2) and sheight when the quotient is smaller sized than the divisor or as soon as a prime variable is found. Tip 3. If the number has a prime aspect, then it is a compowebsite number. If it has actually no prime factors, then the number is prime.

Example (PageIndex8): prime or composite

Identify each number as prime or composite:

(83) (77)

Solution

Test each prime, in order, to see if it is a factor of (83), beginning through (2), as presented. We will certainly speak once the quotient is smaller than the divisor. Prime Test Factor of 83?
2 Last digit of 83 is not 0, 2, 4, 6, or 8. No.
3 8 + 3 = 11, and 11 is not divisible by 3. No.
5 The last digit of 83 is not 5 or 0. No.
7 83 ÷ 7 = 11.857…. No.
11 83 ÷ 11 = 7.545… No.

We have the right to sheight once we gain to (11) because the quotient ((7.545…)) is much less than the divisor. We did not find any kind of prime numbers that are determinants of (83), so we understand (83) is prime.

Test each prime, in order, to see if it is a element of (77). Prime Test Factor of 77?
2 Last digit is not 0, 2, 4, 6, or 8. No.
3 7 + 7 = 14, and also 14 is not divisible by 3. No.
5 The last digit is not 5 or 0. No.
7 77 ÷ 7 = 11 Yes.

Due to the fact that (77) is divisible by (7), we recognize it is not a prime number. It is composite.

Exercise (PageIndex15)

Identify the number as prime or composite: (91)

composite

## Key Concepts

Divisibility Tests
A number is divisible by
2 if the last digit is 0, 2, 4, 6, or 8
3 if the amount of the digits is divisible by 3
5 if the last digit is 5 or 0
6 if divisible by both 2 and also 3
10 if the last digit is 0
Factors If (acdot b = m), then (a) and (b) are factors of (m), and (m) is the product of (a) and (b). Find all the components of a counting number. Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor. If the quotient is a counting number, the divisor and quotient are a pair of components. If the quotient is not a counting number, the divisor is not a factor. List all the factor pairs. Write all the determinants in order from smallest to largest. Determine if a number is prime. Test each of the primes, in order, to see if it is a element of the number. Start via (2) and sheight when the quotient is smaller than the divisor or when a prime element is found. If the number has a prime factor, then it is a composite number. If it has no prime factors, then the number is prime.

### Identify Multiples of Numbers

In the following exercises, list all the multiples much less than 50 for the provided number.

2 3 4 5 6 7 8 9 10 12

### Use Common Divisibility Tests

In the adhering to exercises, usage the divisibility tests to identify whether each number is divisible by 2, 3, 4, 5, 6, and also 10.

### Find All the Factors of a Number

In the following exercises, discover all the components of the given number.

36 42 60 48 144 200 588 576

## Everyday tennis2007.org

Banking Frank’s grandmommy provided him \$100 at his high college graduation. Instead of spfinishing it, Frank opened up a financial institution account. Eextremely week, he added \$15 to the account. The table shows just how a lot money Frank had put in the account by the finish of each week. Complete the table by filling in the blanks.

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Weeks after graduation Total variety of dollars Frank put in the account Simplified Total
0 100 100
1 100 + 15 115
2 100 + 15 • 2 130
3 100 + 15 • 3
4 100 + 15 • <>
5 100 + <>
6
20
x
Banking In March, Gina opened a Christmas club savings account at her financial institution. She deposited \$75 to open up the account. Eincredibly week, she added \$20 to the account. The table mirrors exactly how much money Gina had actually put in the account by the finish of each week. Complete the table by filling in the blanks. Weeks after opening the account Total variety of dollars Gina put in the account Simplified Total
0 75 75
1 75 + 20 95
2 75 + 20 • 2 115
3 75 + 20 • 3
4 75 + 20 • <>
5 75 + <>
6
20
x

## Writing Exercises

If a number is divisible by 2 and by 3, why is it likewise divisible by 6? What is the distinction in between prime numbers and also compowebsite numbers?