The number 40872
40872 is a composite number with 32 divisors. Its prime factorisation is × 3 × 13 × 131. Divisors (32): 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 131, 156 … 40872.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40872: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
40872 is composite. Its prime factorisation is
- 3
The divisors add up to 110880; without 40872 itself that is 70008, so 40872 is abundant (70008 is more than 40872). Euler's totient φ(40872) = 12480 numbers up to 40872 share no factor with it.
- 4
The digits of 40872 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40872 = 2^{3} \times 3 \times 13 \times 131 \]40872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 110880 |
| Euler totient φ(n) | 12480 |
| Square | 1670520384 |
| Cube | 68277509134848 |
| Square root | 202.168247 (= 2√10218) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 62 |
| Scientific notation | 4.0872 × |
40872 in other forms
| Form | Value |
|---|---|
| In words | forty thousand eight hundred and seventy-two |
| Binary (base 2) | 1001111110101000 |
| Octal (base 8) | 117650 |
| Hexadecimal (base 16) | 9FA8 |
| Base 3 | 2002001210 |
| As time | 40872 seconds = 11 h 21 min 12 s |
Is 40872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40872 ÷ 2 = 20436) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40872 ÷ 3 = 13624) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40872 ÷ 4 = 10218) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40872 ÷ 6 = 6812) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (40872 ÷ 8 = 5109) | 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 2) | 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 (40872 ÷ 12 = 3406) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40872 a prime number?
No. 40872 = × 3 × 13 × 131, so it is divisible by 2.
What are the factors of 40872?
1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 131, 156, 262, 312, 393, 524, 786, 1048, 1572, 1703, 3144, 3406, 5109, 6812, 10218, 13624, 20436, 40872.
What is 40872 in binary?
1001111110101000 (hexadecimal 9FA8, octal 117650).
What is the square root of 40872?
About 202.1682, exactly 2√10218.
Is 40872 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 40872?
40872 is a happy number: repeatedly adding the squares of its digits reaches 1.