The number 13400
13400 is a composite number with 24 divisors. Its prime factorisation is × × 67. Divisors (24): 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 134, 200, 268, 335 … 13400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 13400: a Harshad number: divisible by its digit sum 8.
- 2
13400 is composite. Its prime factorisation is
- 3
The divisors add up to 31620; without 13400 itself that is 18220, so 13400 is abundant (18220 is more than 13400). Euler's totient φ(13400) = 5280 numbers up to 13400 share no factor with it.
- 4
The digits of 13400 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 13400 = 2^{3} \times 5^{2} \times 67 \]13400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 31620 |
| Euler totient φ(n) | 5280 |
| Square | 179560000 |
| Cube | 2406104000000 |
| Square root | 115.758369 (= 10√134) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 138 |
| Scientific notation | 1.34 × |
13400 in other forms
| Form | Value |
|---|---|
| In words | thirteen thousand four hundred |
| Binary (base 2) | 11010001011000 |
| Octal (base 8) | 32130 |
| Hexadecimal (base 16) | 3458 |
| Base 3 | 200101022 |
| As time | 13400 seconds = 3 h 43 min 20 s |
Is 13400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (13400 ÷ 2 = 6700) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (13400 ÷ 4 = 3350) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (13400 ÷ 5 = 2680) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (13400 ÷ 8 = 1675) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (13400 ÷ 10 = 1340) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 13400 a prime number?
No. 13400 = × × 67, so it is divisible by 2.
What are the factors of 13400?
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 134, 200, 268, 335, 536, 670, 1340, 1675, 2680, 3350, 6700, 13400.
What is 13400 in binary?
11010001011000 (hexadecimal 3458, octal 32130).
What is the square root of 13400?
About 115.7584, exactly 10√134.
Is 13400 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 13400?
13400 is a Harshad number: divisible by its digit sum 8.