The number 37872
37872 is a composite number with 30 divisors. Its prime factorisation is × × 263. Divisors (30): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 263 … 37872.
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How to work it out
- 1
37872 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
37872 is composite. Its prime factorisation is
- 3
The divisors add up to 106392; without 37872 itself that is 68520, so 37872 is abundant (68520 is more than 37872). Euler's totient φ(37872) = 12576 numbers up to 37872 share no factor with it.
- 4
The digits of 37872 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 93 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37872 = 2^{4} \times 3^{2} \times 263 \]37872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 30 |
| Sum of divisors | 106392 |
| Euler totient φ(n) | 12576 |
| Square | 1434288384 |
| Cube | 54319369678848 |
| Square root | 194.607297 (= 12√263) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 93 |
| Scientific notation | 3.7872 × |
37872 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand eight hundred and seventy-two |
| Binary (base 2) | 1001001111110000 |
| Octal (base 8) | 111760 |
| Hexadecimal (base 16) | 93F0 |
| Base 3 | 1220221200 |
| As time | 37872 seconds = 10 h 31 min 12 s |
Is 37872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37872 ÷ 2 = 18936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37872 ÷ 3 = 12624) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37872 ÷ 4 = 9468) | 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 (37872 ÷ 6 = 6312) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (37872 ÷ 8 = 4734) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (37872 ÷ 9 = 4208) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37872 ÷ 12 = 3156) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37872 a prime number?
No. 37872 = × × 263, so it is divisible by 2.
What are the factors of 37872?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 263, 526, 789, 1052, 1578, 2104, 2367, 3156, 4208, 4734, 6312, 9468, 12624, 18936, 37872.
What is 37872 in binary?
1001001111110000 (hexadecimal 93F0, octal 111760).
What is the square root of 37872?
About 194.6073, exactly 12√263.
Is 37872 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 37872?
It is a composite number with 30 divisors.