The number 9980
9980 is a composite number with 12 divisors. Its prime factorisation is × 5 × 499. Divisors (12): 1, 2, 4, 5, 10, 20, 499, 998, 1996, 2495, 4990, 9980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 9980: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
9980 is composite. Its prime factorisation is
- 3
The divisors add up to 21000; without 9980 itself that is 11020, so 9980 is abundant (11020 is more than 9980). Euler's totient φ(9980) = 3984 numbers up to 9980 share no factor with it.
- 4
The digits of 9980 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 9980 = 2^{2} \times 5 \times 499 \]9980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 21000 |
| Euler totient φ(n) | 3984 |
| Square | 99600400 |
| Cube | 994011992000 |
| Square root | 99.899950 (= 2√2495) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 73 |
| Scientific notation | 9.98 × |
9980 in other forms
| Form | Value |
|---|---|
| In words | nine thousand nine hundred and eighty |
| Binary (base 2) | 10011011111100 |
| Octal (base 8) | 23374 |
| Hexadecimal (base 16) | 26FC |
| Base 3 | 111200122 |
| As time | 9980 seconds = 2 h 46 min 20 s |
Is 9980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (9980 ÷ 2 = 4990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (9980 ÷ 4 = 2495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (9980 ÷ 5 = 1996) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (9980 ÷ 10 = 998) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 9980 a prime number?
No. 9980 = × 5 × 499, so it is divisible by 2.
What are the factors of 9980?
1, 2, 4, 5, 10, 20, 499, 998, 1996, 2495, 4990, 9980.
What is 9980 in binary?
10011011111100 (hexadecimal 26FC, octal 23374).
What is the square root of 9980?
About 99.8999, exactly 2√2495.
Is 9980 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 9980?
9980 is a happy number: repeatedly adding the squares of its digits reaches 1.