The number 630
630 is a triangular number: 1 + 2 + … + 35 = 630. Its prime factorisation is 2 × × 5 × 7. Divisors (24): 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45 … 630.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 630: a triangular number: 1 + 2 + … + 35 = 630; a Harshad number: divisible by its digit sum 9.
- 2
630 is composite. Its prime factorisation is
- 3
The divisors add up to 1872; without 630 itself that is 1242, so 630 is abundant (1242 is more than 630). Euler's totient φ(630) = 144 numbers up to 630 share no factor with it.
- 4
The digits of 630 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 38 steps to reach 1.
LaTeX source of the formulas on this page
\[ 630 = 2 \times 3^{2} \times 5 \times 7 \]630 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 1872 |
| Euler totient φ(n) | 144 |
| Square | 396900 |
| Cube | 250047000 |
| Square root | 25.099801 (= 3√70) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 38 |
| Scientific notation | 6.3 × |
630 in other forms
| Form | Value |
|---|---|
| In words | six hundred and thirty |
| Roman numerals | DCXXX |
| Binary (base 2) | 1001110110 |
| Octal (base 8) | 1166 |
| Hexadecimal (base 16) | 276 |
| Base 3 | 212100 |
| As time | 630 seconds = 10 min 30 s |
Is 630 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (630 ÷ 2 = 315) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (630 ÷ 3 = 210) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (630 ÷ 5 = 126) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (630 ÷ 6 = 105) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (630 ÷ 7 = 90) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (630 ÷ 9 = 70) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (630 ÷ 10 = 63) | 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 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 630 a prime number?
No. 630 = 2 × × 5 × 7, so it is divisible by 2.
What are the factors of 630?
1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630.
What is 630 in binary?
1001110110 (hexadecimal 276, octal 1166).
What is the square root of 630?
About 25.0998, exactly 3√70.
What is 630 in Roman numerals?
DCXXX.
Is 630 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 630?
630 is a triangular number: 1 + 2 + … + 35 = 630; a Harshad number: divisible by its digit sum 9.