The number 7980
7980 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 7 × 19. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 28, 30 … 7980.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
7980 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
7980 is composite. Its prime factorisation is
- 3
The divisors add up to 26880; without 7980 itself that is 18900, so 7980 is abundant (18900 is more than 7980). Euler's totient φ(7980) = 1728 numbers up to 7980 share no factor with it.
- 4
The digits of 7980 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 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7980 = 2^{2} \times 3 \times 5 \times 7 \times 19 \]7980 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 26880 |
| Euler totient φ(n) | 1728 |
| Square | 63680400 |
| Cube | 508169592000 |
| Square root | 89.330846 (= 2√1995) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 52 |
| Scientific notation | 7.98 × |
7980 in other forms
| Form | Value |
|---|---|
| In words | seven thousand nine hundred and eighty |
| Binary (base 2) | 1111100101100 |
| Octal (base 8) | 17454 |
| Hexadecimal (base 16) | 1F2C |
| Base 3 | 101221120 |
| As time | 7980 seconds = 2 h 13 min 0 s |
Is 7980 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7980 ÷ 2 = 3990) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7980 ÷ 3 = 2660) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7980 ÷ 4 = 1995) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7980 ÷ 5 = 1596) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7980 ÷ 6 = 1330) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7980 ÷ 7 = 1140) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7980 ÷ 10 = 798) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (7980 ÷ 12 = 665) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7980 a prime number?
No. 7980 = × 3 × 5 × 7 × 19, so it is divisible by 2.
What are the factors of 7980?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 28, 30, 35, 38, 42, 57, 60, 70, 76, 84, 95, 105, 114, 133, 140, 190, 210, 228, 266, 285, 380, 399, 420, 532, 570, 665, 798, 1140, 1330, 1596, 1995, 2660, 3990, 7980.
What is 7980 in binary?
1111100101100 (hexadecimal 1F2C, octal 17454).
What is the square root of 7980?
About 89.3308, exactly 2√1995.
Is 7980 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 7980?
It is a composite number with 48 divisors.