The number 9870
9870 is a triangular number: 1 + 2 + … + 140 = 9870. Its prime factorisation is 2 × 3 × 5 × 7 × 47. Divisors (32): 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 47, 70, 94 … 9870.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9870: a triangular number: 1 + 2 + … + 140 = 9870.
- 2
9870 is composite. Its prime factorisation is
- 3
The divisors add up to 27648; without 9870 itself that is 17778, so 9870 is abundant (17778 is more than 9870). Euler's totient φ(9870) = 2208 numbers up to 9870 share no factor with it.
- 4
The digits of 9870 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 197 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9870 = 2 \times 3 \times 5 \times 7 \times 47 \]
9870 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 27648 |
| Euler totient φ(n) | 2208 |
| Square | 97416900 |
| Cube | 961504803000 |
| Square root | 99.347874 |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 197 |
| Scientific notation | 9.87 × |
9870 in other forms
| Form | Value |
|---|---|
| In words | nine thousand eight hundred and seventy |
| Binary (base 2) | 10011010001110 |
| Octal (base 8) | 23216 |
| Hexadecimal (base 16) | 268E |
| Base 3 | 111112120 |
| As time | 9870 seconds = 2 h 44 min 30 s |
Is 9870 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9870 ÷ 2 = 4935) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (9870 ÷ 3 = 3290) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9870 ÷ 5 = 1974) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (9870 ÷ 6 = 1645) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (9870 ÷ 7 = 1410) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9870 ÷ 10 = 987) | 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 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9870 a prime number?
No. 9870 = 2 × 3 × 5 × 7 × 47, so it is divisible by 2.
What are the factors of 9870?
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 47, 70, 94, 105, 141, 210, 235, 282, 329, 470, 658, 705, 987, 1410, 1645, 1974, 3290, 4935, 9870.
What is 9870 in binary?
10011010001110 (hexadecimal 268E, octal 23216).
What is the square root of 9870?
About 99.3479.
Is 9870 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 9870?
9870 is a triangular number: 1 + 2 + … + 140 = 9870.