Even and odd, multiples, factors and prime numbers. Play with numbers, solve missions, crack detective puzzles and beat the clock.
Even and odd. Put dots in pairs. If every dot has a partner, the number is even. If one dot is left alone, it is odd. Even numbers end in 0, 2, 4, 6 or 8.
Multiples. Skip count by 5 and you say 5, 10, 15, 20. Those are the multiples of 5. On a number chart they make a neat pattern.
Factors. A factor divides a number with nothing left over. The factors of 12 are 1, 2, 3, 4, 6 and 12. A factor pair is two numbers that multiply to make it, such as 3 × 4. Each pair is also a rectangle of dots: 3 rows of 4.
Prime and composite. A prime number has exactly two factors: 1 and itself, like 7. A composite number has more than two, like 12. The number 1 is neither, because it has only one factor. The number 2 is the only even prime.
The sieve. Write the numbers 1 to 100. Keep 2 and cross out its multiples. Keep the next number left, 3, and cross out its multiples. Keep going. The numbers that are never crossed out are the primes. This old trick is the sieve of Eratosthenes.
Factor trees and rules. Split a number into a pair of factors again and again until every end is prime. That gives its prime factors, for example 60 = 2 × 2 × 3 × 5. Divisibility rules are shortcuts: a number is divisible by 3 if its digits add up to a multiple of 3, and by 9 if its digits add up to a multiple of 9. The greatest common factor (GCF) is the biggest factor two numbers share. The least common multiple (LCM) is the smallest number they both divide into.
Try this above. In the Number Lab look at 12, then 13, then 1 and 2. Open the sieve and press Next prime until it finishes. How many primes are there up to 100?
No. A prime has exactly two different factors, and 1 has only one. So 1 is neither prime nor composite.
Every other even number can be divided by 2, so it has 2 as an extra factor. That gives it more than two factors, so it is composite.
Factors divide a number (3 is a factor of 12). Multiples are what you get by skip counting (12 is a multiple of 3).
"Just starting" covers even and odd, and multiples of 2, 5 and 10. "I know the basics" covers factors, prime numbers and the sieve. "Challenge me" adds factor trees, divisibility rules, GCF and LCM.
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