The number 10980
10980 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 61. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 10980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10980: a Harshad number: divisible by its digit sum 18.
- 2
10980 is composite. Its prime factorisation is
- 3
The divisors add up to 33852; without 10980 itself that is 22872, so 10980 is abundant (22872 is more than 10980). Euler's totient φ(10980) = 2880 numbers up to 10980 share no factor with it.
- 4
The digits of 10980 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10980 = 2^{2} \times 3^{2} \times 5 \times 61 \]10980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 33852 |
| Euler totient φ(n) | 2880 |
| Square | 120560400 |
| Cube | 1323753192000 |
| Square root | 104.785495 (= 6√305) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.098 × |
10980 in other forms
| Form | Value |
|---|---|
| In words | ten thousand nine hundred and eighty |
| Binary (base 2) | 10101011100100 |
| Octal (base 8) | 25344 |
| Hexadecimal (base 16) | 2AE4 |
| Base 3 | 120001200 |
| As time | 10980 seconds = 3 h 3 min 0 s |
Is 10980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10980 ÷ 2 = 5490) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10980 ÷ 3 = 3660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10980 ÷ 4 = 2745) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10980 ÷ 5 = 2196) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10980 ÷ 6 = 1830) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (10980 ÷ 9 = 1220) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10980 ÷ 10 = 1098) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10980 ÷ 12 = 915) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10980 a prime number?
No. 10980 = × × 5 × 61, so it is divisible by 2.
What are the factors of 10980?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 61, 90, 122, 180, 183, 244, 305, 366, 549, 610, 732, 915, 1098, 1220, 1830, 2196, 2745, 3660, 5490, 10980.
What is 10980 in binary?
10101011100100 (hexadecimal 2AE4, octal 25344).
What is the square root of 10980?
About 104.7855, exactly 6√305.
Is 10980 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 10980?
10980 is a Harshad number: divisible by its digit sum 18.