The number 84
84 is a composite number with 12 divisors. Its prime factorisation is × 3 × 7. Divisors (12): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 84: a Harshad number: divisible by its digit sum 12.
- 2
84 is composite. Its prime factorisation is
- 3
The divisors add up to 224; without 84 itself that is 140, so 84 is abundant (140 is more than 84). Euler's totient φ(84) = 24 numbers up to 84 share no factor with it.
- 4
The digits of 84 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 9 steps to reach 1.
LaTeX source of the formulas on this page
\[ 84 = 2^{2} \times 3 \times 7 \]84 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 224 |
| Euler totient φ(n) | 24 |
| Square | 7056 |
| Cube | 592704 |
| Square root | 9.165151 (= 2√21) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 9 |
| Scientific notation | 8.4 × |
84 in other forms
| Form | Value |
|---|---|
| In words | eighty-four |
| Roman numerals | LXXXIV |
| Binary (base 2) | 1010100 |
| Octal (base 8) | 124 |
| Hexadecimal (base 16) | 54 |
| Base 3 | 10010 |
| As time | 84 seconds = 1 min 24 s |
Is 84 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (84 ÷ 2 = 42) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (84 ÷ 3 = 28) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (84 ÷ 4 = 21) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (84 ÷ 6 = 14) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (84 ÷ 7 = 12) | 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 | No (remainder 4) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (84 ÷ 12 = 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 84 a prime number?
No. 84 = × 3 × 7, so it is divisible by 2.
What are the factors of 84?
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
What is 84 in binary?
1010100 (hexadecimal 54, octal 124).
What is the square root of 84?
About 9.1652, exactly 2√21.
What is 84 in Roman numerals?
LXXXIV.
Is 84 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 84?
84 is a Harshad number: divisible by its digit sum 12.