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約数の計算機：ある数のすべての約数

この約数計算機は整数のすべての約数を一覧にします（26 の約数は 1、2、13、26）。約数のペア、約数の個数、素因数分解もあわせて示します。1 兆までの数に対応しています。

結果

値を入力して「計算」を押すと結果が表示されます。

公式

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.

この計算ツールの使い方

  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.

解き方付き例題

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.

よくある間違い

  • 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…

よくある質問

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.