Formules

Calculatrice de diviseurs : tous les diviseurs d’un nombre

Cette calculatrice liste tous les diviseurs d’un entier — les diviseurs de 26 sont 1, 2, 13 et 26 — avec les paires de diviseurs, leur nombre et la décomposition en facteurs premiers. Elle fonctionne jusqu’à mille milliards.

Résultat

Saisissez les valeurs et appuyez sur Calculer pour voir le résultat.

Formule

n=a×b  ⇒  a and b are factors of nn = a \times b \;\Rightarrow\; a \text{ and } b \text{ are factors of } n

Factors come in pairs; you only need to test divisors up to √n.

n=p1e1p2e2⋯  ⇒  #factors=(e1+1)(e2+1)⋯n = p_1^{e_1} p_2^{e_2} \cdots \;\Rightarrow\; \#\text{factors} = (e_1 + 1)(e_2 + 1)\cdots

The number of factors from the prime factorization.

Comment utiliser cette calculatrice

  1. Type a positive whole number.
  2. Press Calculate to see all its factors, the factor pairs, the number of factors and the prime factorization.
  3. The steps test each number up to √n, so you can follow the method by hand.

Exemples corrigés

All factors of 26

Test 1 to √26 ≈ 5.1: 1 × 26 and 2 × 13 work; 3, 4 and 5 don’t divide 26.

So the factors of 26 are 1, 2, 13 and 26.

Prime factorization: 26 = 2 × 13.

Factors of 54

Pairs up to √54 ≈ 7.3: 1 × 54, 2 × 27, 3 × 18, 6 × 9.

Factors: 1, 2, 3, 6, 9, 18, 27, 54.

54 = 2 × 3³, and (1 + 1)(3 + 1) = 8 factors ✓.

A square number: 36

Pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6 — the 6 is only counted once.

So 36 has 9 factors, an odd number, as every square does.

Erreurs fréquentes

  • Forgetting 1 and the number itself — they are always factors.
  • Stopping too early: test every whole number up to √n.
  • Counting a square root twice: 6 × 6 gives one factor, 6.
  • Confusing factors with multiples: factors of 26 divide it; multiples of 26 are 26, 52, 78…

Questions fréquentes

What are all the factors of 26?

1, 2, 13 and 26. The factor pairs are 1 × 26 and 2 × 13, and 26 = 2 × 13 in primes.

How do I find all the factors of a number?

Divide it by 1, 2, 3, … up to its square root. Every division with no remainder gives a factor pair; list both numbers in each pair.

What is the difference between factors and prime factors?

Factors are all the numbers that divide n exactly. Prime factors are only the primes among them, multiplied together to make n: the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, but its prime factorization is 2³ × 3.