The number 51072
51072 is a composite number with 64 divisors. Its prime factorisation is × 3 × 7 × 19. Divisors (64): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 32, 38 … 51072.
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How to work it out
- 1
What is special about 51072: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
51072 is composite. Its prime factorisation is
- 3
The divisors add up to 163200; without 51072 itself that is 112128, so 51072 is abundant (112128 is more than 51072). Euler's totient φ(51072) = 13824 numbers up to 51072 share no factor with it.
- 4
The digits of 51072 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51072 = 2^{7} \times 3 \times 7 \times 19 \]51072 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 163200 |
| Euler totient φ(n) | 13824 |
| Square | 2608349184 |
| Cube | 133213609525248 |
| Square root | 225.991150 (= 8√798) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 127 |
| Scientific notation | 5.1072 × |
51072 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand and seventy-two |
| Binary (base 2) | 1100011110000000 |
| Octal (base 8) | 143600 |
| Hexadecimal (base 16) | C780 |
| Base 3 | 2121001120 |
| As time | 51072 seconds = 14 h 11 min 12 s |
Is 51072 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51072 ÷ 2 = 25536) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51072 ÷ 3 = 17024) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51072 ÷ 4 = 12768) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (51072 ÷ 6 = 8512) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (51072 ÷ 7 = 7296) | 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 (51072 ÷ 8 = 6384) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (51072 ÷ 12 = 4256) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51072 a prime number?
No. 51072 = × 3 × 7 × 19, so it is divisible by 2.
What are the factors of 51072?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 32, 38, 42, 48, 56, 57, 64, 76, 84, 96, 112, 114, 128, 133, 152, 168, 192, 224, 228, 266, 304, 336, 384, 399, 448, 456, 532, 608, 672, 798, 896, 912, 1064, 1216, 1344, 1596, 1824, 2128, 2432, 2688, 3192, 3648, 4256, 6384, 7296, 8512, 12768, 17024, 25536, 51072.
What is 51072 in binary?
1100011110000000 (hexadecimal C780, octal 143600).
What is the square root of 51072?
About 225.9912, exactly 8√798.
Is 51072 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 51072?
51072 is a happy number: repeatedly adding the squares of its digits reaches 1.