Grades 3–5NumberPlanned

Factors, multiples and primes

Factors and multiples, divisibility tests, prime and composite numbers, and writing numbers as products of primes.

math.number.factors-primes

The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.

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Required prerequisites, all the way down: 4

List the factors of numbers up to 100 and find common factors and common multiples.
Classify numbers as prime or composite and use the sieve of Eratosthenes.
Write a whole number as a product of primes using a factor tree, and explain the divisibility tests for 2, 3, 5, 9 and 10.

b is a factor of a, and a is a multiple of b, if a = b × k for some whole number k.
A prime is a whole number greater than 1 whose only factors are 1 and itself; a composite number is a whole number greater than 1 that is not prime.

Every whole number greater than 1 is a prime or a product of primes, and the product is unique apart from order (the fundamental theorem of arithmetic, proved later).
A number is divisible by 3 (or by 9) exactly when the sum of its digits is.
1 is neither prime nor composite.

Cryptography RSA encryption relies on the belief, widely held but not proved, that factoring very large numbers is computationally hard.
Rings, ideals and fields Unique factorisation can fail in other number systems: in ℤ[√−5], 6 = 2 · 3 = (1 + √−5)(1 − √−5).