The number 7000
7000 is a composite number with 32 divisors. Its prime factorisation is × × 7. Divisors (32): 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70 … 7000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7000: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 7.
- 2
7000 is composite. Its prime factorisation is
- 3
The divisors add up to 18720; without 7000 itself that is 11720, so 7000 is abundant (11720 is more than 7000). Euler's totient φ(7000) = 2400 numbers up to 7000 share no factor with it.
- 4
The digits of 7000 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7000 = 2^{3} \times 5^{3} \times 7 \]7000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 18720 |
| Euler totient φ(n) | 2400 |
| Square | 49000000 |
| Cube | 343000000000 |
| Square root | 83.666003 (= 10√70) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 31 |
| Scientific notation | 7 × |
7000 in other forms
| Form | Value |
|---|---|
| In words | seven thousand |
| Binary (base 2) | 1101101011000 |
| Octal (base 8) | 15530 |
| Hexadecimal (base 16) | 1B58 |
| Base 3 | 100121021 |
| As time | 7000 seconds = 1 h 56 min 40 s |
Is 7000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7000 ÷ 2 = 3500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7000 ÷ 4 = 1750) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7000 ÷ 5 = 1400) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7000 ÷ 7 = 1000) | 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 | Yes (7000 ÷ 8 = 875) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (7000 ÷ 10 = 700) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7000 a prime number?
No. 7000 = × × 7, so it is divisible by 2.
What are the factors of 7000?
1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000.
What is 7000 in binary?
1101101011000 (hexadecimal 1B58, octal 15530).
What is the square root of 7000?
About 83.6660, exactly 10√70.
Is 7000 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 7000?
7000 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 7.