The number 1260
1260 is a highly composite number: it has 36 divisors, more than any smaller number. Its prime factorisation is × × 5 × 7. Divisors (36): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28 … 1260.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1260: a highly composite number: it has 36 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.
- 2
1260 is composite. Its prime factorisation is
- 3
The divisors add up to 4368; without 1260 itself that is 3108, so 1260 is abundant (3108 is more than 1260). Euler's totient φ(1260) = 288 numbers up to 1260 share no factor with it.
- 4
The digits of 1260 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 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1260 = 2^{2} \times 3^{2} \times 5 \times 7 \]1260 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 4368 |
| Euler totient φ(n) | 288 |
| Square | 1587600 |
| Cube | 2000376000 |
| Square root | 35.496479 (= 6√35) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 39 |
| Scientific notation | 1.26 × |
1260 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and sixty |
| Roman numerals | MCCLX |
| Binary (base 2) | 10011101100 |
| Octal (base 8) | 2354 |
| Hexadecimal (base 16) | 4EC |
| Base 3 | 1201200 |
| As time | 1260 seconds = 21 min 0 s |
Is 1260 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1260 ÷ 2 = 630) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1260 ÷ 3 = 420) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1260 ÷ 4 = 315) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1260 ÷ 5 = 252) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1260 ÷ 6 = 210) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (1260 ÷ 7 = 180) | 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 | Yes (1260 ÷ 9 = 140) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1260 ÷ 10 = 126) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (1260 ÷ 12 = 105) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1260 a prime number?
No. 1260 = × × 5 × 7, so it is divisible by 2.
What are the factors of 1260?
1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.
What is 1260 in binary?
10011101100 (hexadecimal 4EC, octal 2354).
What is the square root of 1260?
About 35.4965, exactly 6√35.
What is 1260 in Roman numerals?
MCCLX.
Is 1260 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1260?
1260 is a highly composite number: it has 36 divisors, more than any smaller number; a Harshad number: divisible by its digit sum 9.