The number 40824
40824 is a composite number with 56 divisors. Its prime factorisation is × × 7. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36 … 40824.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40824: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
40824 is composite. Its prime factorisation is
- 3
The divisors add up to 131160; without 40824 itself that is 90336, so 40824 is abundant (90336 is more than 40824). Euler's totient φ(40824) = 11664 numbers up to 40824 share no factor with it.
- 4
The digits of 40824 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 88 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40824 = 2^{3} \times 3^{6} \times 7 \]40824 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 131160 |
| Euler totient φ(n) | 11664 |
| Square | 1666598976 |
| Cube | 68037236596224 |
| Square root | 202.049499 (= 54√14) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 88 |
| Scientific notation | 4.0824 × |
40824 in other forms
| Form | Value |
|---|---|
| In words | forty thousand eight hundred and twenty-four |
| Binary (base 2) | 1001111101111000 |
| Octal (base 8) | 117570 |
| Hexadecimal (base 16) | 9F78 |
| Base 3 | 2002000000 |
| As time | 40824 seconds = 11 h 20 min 24 s |
Is 40824 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40824 ÷ 2 = 20412) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40824 ÷ 3 = 13608) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40824 ÷ 4 = 10206) | 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 (40824 ÷ 6 = 6804) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (40824 ÷ 7 = 5832) | 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 (40824 ÷ 8 = 5103) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (40824 ÷ 9 = 4536) | 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 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (40824 ÷ 12 = 3402) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40824 a prime number?
No. 40824 = × × 7, so it is divisible by 2.
What are the factors of 40824?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 81, 84, 108, 126, 162, 168, 189, 216, 243, 252, 324, 378, 486, 504, 567, 648, 729, 756, 972, 1134, 1458, 1512, 1701, 1944, 2268, 2916, 3402, 4536, 5103, 5832, 6804, 10206, 13608, 20412, 40824.
What is 40824 in binary?
1001111101111000 (hexadecimal 9F78, octal 117570).
What is the square root of 40824?
About 202.0495, exactly 54√14.
Is 40824 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 40824?
40824 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.