The number 840
840 is a highly composite number: it has 32 divisors, more than any smaller number. Its prime factorisation is × 3 × 5 × 7. Divisors (32): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28 … 840.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 840: a highly composite number: it has 32 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 12.
- 2
840 is composite. Its prime factorisation is
- 3
The divisors add up to 2880; without 840 itself that is 2040, so 840 is abundant (2040 is more than 840). Euler's totient φ(840) = 192 numbers up to 840 share no factor with it.
- 4
The digits of 840 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 840 = 2^{3} \times 3 \times 5 \times 7 \]840 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 2880 |
| Euler totient φ(n) | 192 |
| Square | 705600 |
| Cube | 592704000 |
| Square root | 28.982753 (= 2√210) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 41 |
| Scientific notation | 8.4 × |
840 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and forty |
| Roman numerals | DCCCXL |
| Binary (base 2) | 1101001000 |
| Octal (base 8) | 1510 |
| Hexadecimal (base 16) | 348 |
| Base 3 | 1011010 |
| As time | 840 seconds = 14 min 0 s |
Is 840 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (840 ÷ 2 = 420) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (840 ÷ 3 = 280) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (840 ÷ 4 = 210) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (840 ÷ 5 = 168) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (840 ÷ 6 = 140) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (840 ÷ 7 = 120) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (840 ÷ 8 = 105) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (840 ÷ 10 = 84) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (840 ÷ 12 = 70) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 840 a prime number?
No. 840 = × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 840?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.
What is 840 in binary?
1101001000 (hexadecimal 348, octal 1510).
What is the square root of 840?
About 28.9828, exactly 2√210.
What is 840 in Roman numerals?
DCCCXL.
Is 840 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 840?
840 is a highly composite number: it has 32 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 12.