The number 21980
21980 is a composite number with 24 divisors. Its prime factorisation is × 5 × 7 × 157. Divisors (24): 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 157, 314, 628, 785 … 21980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21980: a Harshad number: divisible by its digit sum 20.
- 2
21980 is composite. Its prime factorisation is
- 3
The divisors add up to 53088; without 21980 itself that is 31108, so 21980 is abundant (31108 is more than 21980). Euler's totient φ(21980) = 7488 numbers up to 21980 share no factor with it.
- 4
The digits of 21980 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 69 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21980 = 2^{2} \times 5 \times 7 \times 157 \]21980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 53088 |
| Euler totient φ(n) | 7488 |
| Square | 483120400 |
| Cube | 10618986392000 |
| Square root | 148.256534 (= 2√5495) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 69 |
| Scientific notation | 2.198 × |
21980 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand nine hundred and eighty |
| Binary (base 2) | 101010111011100 |
| Octal (base 8) | 52734 |
| Hexadecimal (base 16) | 55DC |
| Base 3 | 1010011002 |
| As time | 21980 seconds = 6 h 6 min 20 s |
Is 21980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21980 ÷ 2 = 10990) | 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 (21980 ÷ 4 = 5495) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21980 ÷ 5 = 4396) | 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 | Yes (21980 ÷ 7 = 3140) | 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 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21980 ÷ 10 = 2198) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21980 a prime number?
No. 21980 = × 5 × 7 × 157, so it is divisible by 2.
What are the factors of 21980?
1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 157, 314, 628, 785, 1099, 1570, 2198, 3140, 4396, 5495, 10990, 21980.
What is 21980 in binary?
101010111011100 (hexadecimal 55DC, octal 52734).
What is the square root of 21980?
About 148.2565, exactly 2√5495.
Is 21980 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 21980?
21980 is a Harshad number: divisible by its digit sum 20.