The number 51264
51264 is a composite number with 42 divisors. Its prime factorisation is × × 89. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 51264.
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How to work it out
- 1
What is special about 51264: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
51264 is composite. Its prime factorisation is
- 3
The divisors add up to 148590; without 51264 itself that is 97326, so 51264 is abundant (97326 is more than 51264). Euler's totient φ(51264) = 16896 numbers up to 51264 share no factor with it.
- 4
The digits of 51264 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 65 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51264 = 2^{6} \times 3^{2} \times 89 \]51264 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 148590 |
| Euler totient φ(n) | 16896 |
| Square | 2627997696 |
| Cube | 134721673887744 |
| Square root | 226.415547 (= 24√89) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 65 |
| Scientific notation | 5.1264 × |
51264 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand two hundred and sixty-four |
| Binary (base 2) | 1100100001000000 |
| Octal (base 8) | 144100 |
| Hexadecimal (base 16) | C840 |
| Base 3 | 2121022200 |
| As time | 51264 seconds = 14 h 14 min 24 s |
Is 51264 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51264 ÷ 2 = 25632) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51264 ÷ 3 = 17088) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51264 ÷ 4 = 12816) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (51264 ÷ 6 = 8544) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (51264 ÷ 8 = 6408) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (51264 ÷ 9 = 5696) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (51264 ÷ 12 = 4272) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51264 a prime number?
No. 51264 = × × 89, so it is divisible by 2.
What are the factors of 51264?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 89, 96, 144, 178, 192, 267, 288, 356, 534, 576, 712, 801, 1068, 1424, 1602, 2136, 2848, 3204, 4272, 5696, 6408, 8544, 12816, 17088, 25632, 51264.
What is 51264 in binary?
1100100001000000 (hexadecimal C840, octal 144100).
What is the square root of 51264?
About 226.4155, exactly 24√89.
Is 51264 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 51264?
51264 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.