Grade 5 (age 10-11)

Primes and Composites

A prime number divides only by 1 and itself, while a composite number has other divisors too. Primes like 2, 3, 5, and 7 cannot be split further and are the building blocks of every number; 1 is neither prime nor composite. The Sieve of Eratosthenes crosses out multiples one after another to leave only the primes. Here you change which multiples to remove, then check a number's divisors to decide prime or composite.

What is a prime?

⭐ Numbers that cannot be split further

①Divisors are only 1 and itself = prime

②2, 3, 5, 7, 11, 13, ... are primes

③1 is not prime (only one divisor)

Sieve of Eratosthenes

Multiples to remove3

🔢 Sieve them out

①Cross out multiples of 2 (4,6,8,...)

②Then multiples of 3 (6,9,12,...)

③Then 5, 7, ... — what's left are primes!

Prime vs. Composite

Number to check12

Summary

Prime

Natural number whose divisors are only 1 and itself

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...

Composite

Natural number with 3+ divisors

4, 6, 8, 9, 10, 12, 14, 15, ...

1 is special

1 is neither prime nor composite

Because it has only 1 divisor

🎯 Key Points

①Prime: 2 divisors (1 and itself)

②Composite: 3+ divisors

③1 is neither

④Smallest prime is 2 (only even prime!)

⑤Sieve of Eratosthenes finds primes efficiently

Examples and Unit Test

Example 1

Is 7 prime or composite?

Find the divisors of 7: only 1 and 7.

It has exactly 2 divisors (1 and itself), so 7 is prime.

▸ Prime

A number with exactly 2 divisors (1 and itself) is prime.

Example 2

Is 12 prime or composite?

Divisors of 12: 1, 2, 3, 4, 6, 12; six in all.

It has 3 or more divisors, so 12 is composite.

▸ Composite

A number with 3 or more divisors is composite.

Unit Test

Which of these is NOT prime?

①2

②3

③9

④11

▸ ③ 9

The divisors of 9 are 1, 3, 9; three of them.

9 has 3 divisors so it is composite; 2, 3, 11 each have 2 divisors and are prime.

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Divisors & Multiples

Mixed Fractions