The number 5360
5360 is a composite number with 20 divisors. Its prime factorisation is × 5 × 67. Divisors (20): 1, 2, 4, 5, 8, 10, 16, 20, 40, 67, 80, 134, 268, 335, 536, 670 … 5360.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5360: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
5360 is composite. Its prime factorisation is
- 3
The divisors add up to 12648; without 5360 itself that is 7288, so 5360 is abundant (7288 is more than 5360). Euler's totient φ(5360) = 2112 numbers up to 5360 share no factor with it.
- 4
The digits of 5360 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 72 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5360 = 2^{4} \times 5 \times 67 \]5360 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 12648 |
| Euler totient φ(n) | 2112 |
| Square | 28729600 |
| Cube | 153990656000 |
| Square root | 73.212021 (= 4√335) |
| Digit sum / digital root | 14 / 5 |
| Collatz steps to 1 | 72 |
| Scientific notation | 5.36 × |
5360 in other forms
| Form | Value |
|---|---|
| In words | five thousand three hundred and sixty |
| Binary (base 2) | 1010011110000 |
| Octal (base 8) | 12360 |
| Hexadecimal (base 16) | 14F0 |
| Base 3 | 21100112 |
| As time | 5360 seconds = 1 h 29 min 20 s |
Is 5360 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5360 ÷ 2 = 2680) | 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 (5360 ÷ 4 = 1340) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5360 ÷ 5 = 1072) | 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 5) | 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 (5360 ÷ 8 = 670) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (5360 ÷ 10 = 536) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5360 a prime number?
No. 5360 = × 5 × 67, so it is divisible by 2.
What are the factors of 5360?
1, 2, 4, 5, 8, 10, 16, 20, 40, 67, 80, 134, 268, 335, 536, 670, 1072, 1340, 2680, 5360.
What is 5360 in binary?
1010011110000 (hexadecimal 14F0, octal 12360).
What is the square root of 5360?
About 73.2120, exactly 4√335.
Is 5360 divisible by 3?
No. Its digits add up to 14, which is not a multiple of 3.
What is special about the number 5360?
5360 is a happy number: repeatedly adding the squares of its digits reaches 1.