The number 53460
53460 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30 … 53460.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 53460: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
53460 is composite. Its prime factorisation is
- 3
The divisors add up to 183456; without 53460 itself that is 129996, so 53460 is abundant (129996 is more than 53460). Euler's totient φ(53460) = 12960 numbers up to 53460 share no factor with it.
- 4
The digits of 53460 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 140 steps to reach 1.
LaTeX source of the formulas on this page
\[ 53460 = 2^{2} \times 3^{5} \times 5 \times 11 \]53460 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 183456 |
| Euler totient φ(n) | 12960 |
| Square | 2857971600 |
| Cube | 152787161736000 |
| Square root | 231.214186 (= 18√165) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 140 |
| Scientific notation | 5.346 × |
53460 in other forms
| Form | Value |
|---|---|
| In words | fifty-three thousand four hundred and sixty |
| Binary (base 2) | 1101000011010100 |
| Octal (base 8) | 150324 |
| Hexadecimal (base 16) | D0D4 |
| Base 3 | 2201100000 |
| As time | 53460 seconds = 14 h 51 min 0 s |
Is 53460 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (53460 ÷ 2 = 26730) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (53460 ÷ 3 = 17820) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (53460 ÷ 4 = 13365) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (53460 ÷ 5 = 10692) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (53460 ÷ 6 = 8910) | 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 | Yes (53460 ÷ 9 = 5940) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (53460 ÷ 10 = 5346) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (53460 ÷ 11 = 4860) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (53460 ÷ 12 = 4455) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 53460 a prime number?
No. 53460 = × × 5 × 11, so it is divisible by 2.
What are the factors of 53460?
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 27, 30, 33, 36, 44, 45, 54, 55, 60, 66, 81, 90, 99, 108, 110, 132, 135, 162, 165, 180, 198, 220, 243, 270, 297, 324, 330, 396, 405, 486, 495, 540, 594, 660, 810, 891, 972, 990, 1188, 1215, 1485, 1620, 1782, 1980, 2430, 2673, 2970, 3564, 4455, 4860, 5346, 5940, 8910, 10692, 13365, 17820, 26730, 53460.
What is 53460 in binary?
1101000011010100 (hexadecimal D0D4, octal 150324).
What is the square root of 53460?
About 231.2142, exactly 18√165.
Is 53460 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 53460?
53460 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.