3.º a 5.º gradoNumberPlanificado
Factors, multiples and primes
Factors and multiples, divisibility tests, prime and composite numbers, and writing numbers as products of primes.
math.number.factors-primes
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Se basa en
Requisitos previos obligatorios, hasta el fondo: 4
Aprenderás a
- 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.
Definición
- 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.
Teorema
- 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.
Errores frecuentes
- Thinking 1 is prime.
- Believing all odd numbers are prime, although 9 = 3 × 3.
- Confusing factors with multiples.
Conduce a
Descubrimientos opcionales
- 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).
Lecturas complementarias
- Hans Magnus Enzensberger, The Number Devil