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For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n , then so is − m . The tables below only list positive divisors.
The result must be divisible by 3. Using the example above: 16,499,205,854,376 has four of the digits 1, 4 and 7 and four of the digits 2, 5 and 8; since 4 − 4 = 0 is a multiple of 3, the number 16,499,205,854,376 is divisible by 3. Subtracting 2 times the last digit from the rest gives a multiple of 3. (Works because 21 is divisible by 3)
[3] It is the third (or second) dodecahedral number, [4] and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28), which makes it the seventh tetrahedral number. [5] The number of divisors of 84 is 12. [6] As no smaller number has more than 12 divisors, 84 is a largely composite number. [7]
[3] It is the least common multiple of the numbers from 1 to 8. [4] It is the smallest number divisible by every natural number from 1 to 10, except 9. It is the largest number k such that all coprime quadratic residues modulo k are squares. In this case, they are 1, 121, 169, 289, 361 and 529. [5] It is an evil number.
A natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For ...
The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).
2 4 ⋅ 3 2 ⋅ 5 ⋅ 7 ⋅ 11 ⋅ 13 : 4,2,1,1,1,1 240 2 2 ⋅ 6 ⋅ 30030 : Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are ...
[3] [4] E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself. The composite numbers up to 150 are: