exercise Makes Perfect

## Identify Prime and Composite Numbers

Some numbers, prefer (72), have plenty of factors. Other numbers, such as (7), have only 2 factors: (1) and also the number. A number with just two determinants is dubbed a prime number. A number with much more than two components is called a composite number. The number (1) is no prime no one composite. It has only one factor, itself.

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Definition: prime Numbers and also Composite Numbers

A element number is a counting number better than (1) who only factors are (1) and also itself.

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

Figure (PageIndex5) perform the counting numbers from (2) v (20) along with their factors. The emphasize numbers room prime, since each has actually only two factors.

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HOW TO: determine IF A NUMBER IS PRIME.

step 1. Test every of the primes, in order, to view if it is a variable of the number. Step 2. Start with (2) and also stop once the quotient is smaller than the divisor or as soon as a prime element is found. Step 3. If the number has a prime factor, climate it is a composite number. If it has no element factors, then the number is prime.

Example (PageIndex8): element or composite

Identify each number as prime or composite:

(83) (77)

Solution

Test each prime, in order, to check out if it is a variable of (83), beginning with (2), together shown. We will certainly stop when the quotient is smaller sized than the divisor. element Test factor of 83?
2 Last number of 83 is not 0, 2, 4, 6, or 8. No.
3 8 + 3 = 11, and also 11 is not divisible by 3. No.
5 The critical digit the 83 is not 5 or 0. No.
7 83 ÷ 7 = 11.857…. No.
11 83 ÷ 11 = 7.545… No.

We have the right to stop as soon as we acquire to (11) since the quotient ((7.545…)) is much less than the divisor. We did not find any kind of prime numbers the are determinants of (83), therefore we know (83) is prime.

Test every prime, in order, to view if that is a variable of (77). element Test element of 77?
2 Last digit is no 0, 2, 4, 6, or 8. No.
3 7 + 7 = 14, and 14 is no divisible through 3. No.
5 The last digit is not 5 or 0. No.
7 77 ÷ 7 = 11 Yes.

Since (77) is divisible by (7), we understand it is not a prime number. It is composite.

Exercise (PageIndex15)

Identify the number as prime or composite: (91)

composite

## Key Concepts

Divisibility test
A number is divisible by
2 if the last digit is 0, 2, 4, 6, or 8
3 if the sum of the digits is divisible through 3
5 if the last digit is 5 or 0
6 if divisible by both 2 and 3
10 if the critical digit is 0
determinants If (acdot b = m), then (a) and (b) are components of (m), and also (m) is the product of (a) and (b). Find all the factors of a count number. divide the number by each of the counting numbers, in order, until the quotient is smaller sized than the divisor. If the quotient is a counting number, the divisor and quotient room a pair that factors. If the quotient is not a counting number, the divisor is not a factor. list all the element pairs. Write all the components in bespeak from the smallest to largest. determine if a number is prime. Test every of the primes, in order, to view if the is a variable of the number. Start with (2) and stop as soon as the quotient is smaller sized than the divisor or when a prime aspect is found. If the number has actually a element factor, climate it is a composite number. If it has no element factors, climate the number is prime.

### Identify Multiples of Numbers

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

2 3 4 5 6 7 8 9 10 12

### Use usual Divisibility Tests

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

### Find every the factors of a Number

In the complying with exercises, discover all the factors of the given number.

36 42 60 48 144 200 588 576

## Everyday gimpppa.org

Banking Frank’s grandmother gave him \$100 at his high college graduation. Rather of security it, Frank opened up a bank account. Every week, he added \$15 to the account. The table shows just how much money Frank had actually put in the account through the finish of each week. Complete the table by filling in the blanks.

See more:
What Does Maybe Mean From A Guy Says Maybe To Hanging Out? What Does A Guy Mean When He Says Maybe

Weeks ~ graduation Total number of dollars Frank placed in the account Simplified full
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 up a Christmas club savings account at her bank. She deposit \$75 to open up the account. Every week, she added \$20 come the account. The table shows exactly how much money Gina had put in the account through the end of each week. Finish the table by filling in the blanks. mainly after opened the account Total variety of dollars Gina put in the account Simplified complete
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 also by 3, why is it additionally divisible by 6? What is the difference in between prime numbers and also composite numbers?