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.
    1. Divide the number by each of the counting numbers, in order, until the quotient is smaller than the divisor.
      1. If the quotient is a counting number, the divisor and quotient are a pair of factors.
      2. If the quotient is not a counting number, the divisor is not a factor.
    2. List all the factor pairs.
    3. Write all the factors in order from smallest to largest.
  • Determine if a number is prime.
    1. Test each of the primes, in order, to see if it is a factor of the number.
    2. Start with 2 and stop when the quotient is smaller than the divisor or when a prime factor is found.
    3. 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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