The number 7
7 is a Mersenne prime ( − 1), a twin prime (5 and 7 are both prime) and the 4th prime number. Its only divisors are 1 and 7.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7: a Mersenne prime ( − 1); a twin prime (5 and 7 are both prime); the 4th prime number; a binary palindrome (111); a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
7 is prime, so its only factors are 1 and 7. It is the 4th prime; the next prime is 11 and the one before is 5.
- 3
The divisors add up to 8; without 7 itself that is 1, so 7 is deficient (1 is less than 7). Euler's totient φ(7) = 6 numbers up to 7 share no factor with it.
- 4
The digits of 7 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 16 steps to reach 1.
7 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 8 |
| Euler totient φ(n) | 6 |
| Square | 49 |
| Cube | 343 |
| Square root | 2.645751 |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 16 |
| Scientific notation | 7 × |
7 in other forms
| Form | Value |
|---|---|
| In words | seven |
| Roman numerals | VII |
| Binary (base 2) | 111 |
| Octal (base 8) | 7 |
| Hexadecimal (base 16) | 7 |
| Base 3 | 21 |
| As time | 7 seconds |
Is 7 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | 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 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7 ÷ 7 = 1) | 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 7) | 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 | No (remainder 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 7) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7 a prime number?
Yes. 7 is divisible only by 1 and itself.
What are the factors of 7?
1, 7.
What is 7 in binary?
111 (hexadecimal 7, octal 7).
What is the square root of 7?
About 2.6458.
What is 7 in Roman numerals?
VII.
Is 7 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 7?
7 is a Mersenne prime ( − 1); a twin prime (5 and 7 are both prime); the 4th prime number; a binary palindrome (111); a happy number: repeatedly adding the squares of its digits reaches 1.