Factors and Multiples
If a and b are whole numbers and a is not 0, then a is a factor of b, if and only if there is a whole number c such that a•c=b. We can also say that a divides b or that b is a multiple of a.
Here is an example of the 6 sentences that represent this:
• 2 is a factor of 20, since 2•10=20
• 10 is a factor of 20, since 10•2=20
• 2 divides 20, since 2•10=20
• 10 divides 20, since 10•2=20
• 20 is a multiple of 2, since 2•10=20
• 20 is a multiple of 10, since 10•2=20
A site that my help is http://www.kwiznet.com/p/takeQuiz.php?ChapterID=732
In class, we also covered divisibility tests. I can't believe that I have never learned these tricks.
By 2: a number is divisible by 2 if the ones digit is divisible by 2
By 5: a number is divisible by 5 if the ones digit is a 5 or 0
By 3 or 9: a number is divisible by 9 if the sum of its digits is divisible by 9, a number is divisible by 3 if the sum of its digits is divisible by 3
By 6: a number is divisible by 6 if it is divisible by both 2 and 3
By 4: a number is divisible by 4 if the last 2 digits are divisible by 4
By 8: a number is divisible by 8 if the last 3 digits are divisible by 8
I like the way that the divisibility tests are demonstrated on http://www.mathgoodies.com/lessons/vol3/divisibility.html
I also found the prime number test really helpful. A number is a prime number if it has exactly 2 factors. Once again, I can't believe that I have never learned this before. The prime number test:
Suppose n is a whole number and k is the smallest whole number such that k•k>n (k²>n). If there is no prime less than k that is a factor of n, then n is a prime number.
Example
51: The largest prime you would need to check as a factor is the one that is ≤ √51≈7.1. The largest prime ≤ 7.1 is 7. So you would only need to check divisibility by 2,3,5,7. It is divisible by 3, so 51 is not prime.
Until later.
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