The number 37128
37128 is a triangular number: 1 + 2 + … + 272 = 37128. Its prime factorisation is × 3 × 7 × 13 × 17. Divisors (64): 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 17, 21, 24, 26, 28, 34 … 37128.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 37128: a triangular number: 1 + 2 + … + 272 = 37128; a Harshad number: divisible by its digit sum 21.
- 2
37128 is composite. Its prime factorisation is
- 3
The divisors add up to 120960; without 37128 itself that is 83832, so 37128 is abundant (83832 is more than 37128). Euler's totient φ(37128) = 9216 numbers up to 37128 share no factor with it.
- 4
The digits of 37128 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
\[ 37128 = 2^{3} \times 3 \times 7 \times 13 \times 17 \]37128 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 120960 |
| Euler totient φ(n) | 9216 |
| Square | 1378488384 |
| Cube | 51180516721152 |
| Square root | 192.686274 (= 2√9282) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.7128 × |
37128 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand one hundred and twenty-eight |
| Binary (base 2) | 1001000100001000 |
| Octal (base 8) | 110410 |
| Hexadecimal (base 16) | 9108 |
| Base 3 | 1212221010 |
| As time | 37128 seconds = 10 h 18 min 48 s |
Is 37128 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37128 ÷ 2 = 18564) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37128 ÷ 3 = 12376) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37128 ÷ 4 = 9282) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37128 ÷ 6 = 6188) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (37128 ÷ 7 = 5304) | 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 (37128 ÷ 8 = 4641) | 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 8) | 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 (37128 ÷ 12 = 3094) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37128 a prime number?
No. 37128 = × 3 × 7 × 13 × 17, so it is divisible by 2.
What are the factors of 37128?
1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 17, 21, 24, 26, 28, 34, 39, 42, 51, 52, 56, 68, 78, 84, 91, 102, 104, 119, 136, 156, 168, 182, 204, 221, 238, 273, 312, 357, 364, 408, 442, 476, 546, 663, 714, 728, 884, 952, 1092, 1326, 1428, 1547, 1768, 2184, 2652, 2856, 3094, 4641, 5304, 6188, 9282, 12376, 18564, 37128.
What is 37128 in binary?
1001000100001000 (hexadecimal 9108, octal 110410).
What is the square root of 37128?
About 192.6863, exactly 2√9282.
Is 37128 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 37128?
37128 is a triangular number: 1 + 2 + … + 272 = 37128; a Harshad number: divisible by its digit sum 21.