The number 51120
51120 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 71. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 51120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 51120: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
51120 is composite. Its prime factorisation is
- 3
The divisors add up to 174096; without 51120 itself that is 122976, so 51120 is abundant (122976 is more than 51120). Euler's totient φ(51120) = 13440 numbers up to 51120 share no factor with it.
- 4
The digits of 51120 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 78 steps to reach 1.
LaTeX source of the formulas on this page
\[ 51120 = 2^{4} \times 3^{2} \times 5 \times 71 \]51120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 174096 |
| Euler totient φ(n) | 13440 |
| Square | 2613254400 |
| Cube | 133589564928000 |
| Square root | 226.097324 (= 12√355) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 78 |
| Scientific notation | 5.112 × |
51120 in other forms
| Form | Value |
|---|---|
| In words | fifty-one thousand one hundred and twenty |
| Binary (base 2) | 1100011110110000 |
| Octal (base 8) | 143660 |
| Hexadecimal (base 16) | C7B0 |
| Base 3 | 2121010100 |
| As time | 51120 seconds = 14 h 12 min 0 s |
Is 51120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (51120 ÷ 2 = 25560) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (51120 ÷ 3 = 17040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (51120 ÷ 4 = 12780) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (51120 ÷ 5 = 10224) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (51120 ÷ 6 = 8520) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (51120 ÷ 8 = 6390) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (51120 ÷ 9 = 5680) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (51120 ÷ 10 = 5112) | 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 | Yes (51120 ÷ 12 = 4260) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 51120 a prime number?
No. 51120 = × × 5 × 71, so it is divisible by 2.
What are the factors of 51120?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 71, 72, 80, 90, 120, 142, 144, 180, 213, 240, 284, 355, 360, 426, 568, 639, 710, 720, 852, 1065, 1136, 1278, 1420, 1704, 2130, 2556, 2840, 3195, 3408, 4260, 5112, 5680, 6390, 8520, 10224, 12780, 17040, 25560, 51120.
What is 51120 in binary?
1100011110110000 (hexadecimal C7B0, octal 143660).
What is the square root of 51120?
About 226.0973, exactly 12√355.
Is 51120 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 51120?
51120 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.