Summary and Key Concepts
Key Concepts
| Divisibility Tests | |
|---|---|
| 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 by 3 |
| 5 | if the last digit is 5 or 0 |
| 6 | if divisible by both 2 and 3 |
| 10 | if the last digit is 0 |
- Factors If \(a\cdot b=m\), then \(a\) and \(b\) are factors of \(m\), and \(m\) is the product of \(a\) and \(b\).
- Find all the factors 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 factors.
- If the quotient is not a counting number, the divisor is not a factor.
- List all the factor pairs.
- Write all the factors in order from smallest to largest.
- Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor.
- Determine if a number is prime.
- Test each of the primes, in order, to see if it is a factor of the number.
- Start with 2 and stop when the quotient is smaller than the divisor or when a prime factor 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.
Glossary
multiple of a number
A number is a multiple of \(n\) if it is the product of a counting number and \(n\).
divisibility
If a number \(m\) is a multiple of \(n\), then we say that \(m\) is divisible by \(n\).
prime number
A prime number is a counting number greater than 1 whose only factors are 1 and itself.
composite number
A composite number is a counting number that is not prime.
This lesson is part of:
The Language of Algebra
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