The number 1380
1380 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 23. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92 … 1380.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1380: a Harshad number: divisible by its digit sum 12.
- 2
1380 is composite. Its prime factorisation is
- 3
The divisors add up to 4032; without 1380 itself that is 2652, so 1380 is abundant (2652 is more than 1380). Euler's totient φ(1380) = 352 numbers up to 1380 share no factor with it.
- 4
The digits of 1380 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1380 = 2^{2} \times 3 \times 5 \times 23 \]1380 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 4032 |
| Euler totient φ(n) | 352 |
| Square | 1904400 |
| Cube | 2628072000 |
| Square root | 37.148351 (= 2√345) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 127 |
| Scientific notation | 1.38 × |
1380 in other forms
| Form | Value |
|---|---|
| In words | one thousand three hundred and eighty |
| Roman numerals | MCCCLXXX |
| Binary (base 2) | 10101100100 |
| Octal (base 8) | 2544 |
| Hexadecimal (base 16) | 564 |
| Base 3 | 1220010 |
| As time | 1380 seconds = 23 min 0 s |
Is 1380 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1380 ÷ 2 = 690) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1380 ÷ 3 = 460) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (1380 ÷ 4 = 345) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1380 ÷ 5 = 276) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (1380 ÷ 6 = 230) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (1380 ÷ 10 = 138) | 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 (1380 ÷ 12 = 115) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1380 a prime number?
No. 1380 = × 3 × 5 × 23, so it is divisible by 2.
What are the factors of 1380?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690, 1380.
What is 1380 in binary?
10101100100 (hexadecimal 564, octal 2544).
What is the square root of 1380?
About 37.1484, exactly 2√345.
What is 1380 in Roman numerals?
MCCCLXXX.
Is 1380 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 1380?
1380 is a Harshad number: divisible by its digit sum 12.