The number 48120
48120 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 401. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 48120.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48120: a Harshad number: divisible by its digit sum 15.
- 2
48120 is composite. Its prime factorisation is
- 3
The divisors add up to 144720; without 48120 itself that is 96600, so 48120 is abundant (96600 is more than 48120). Euler's totient φ(48120) = 12800 numbers up to 48120 share no factor with it.
- 4
The digits of 48120 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 158 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48120 = 2^{3} \times 3 \times 5 \times 401 \]48120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 144720 |
| Euler totient φ(n) | 12800 |
| Square | 2315534400 |
| Cube | 111423515328000 |
| Square root | 219.362713 (= 2√12030) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 158 |
| Scientific notation | 4.812 × |
48120 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand one hundred and twenty |
| Binary (base 2) | 1011101111111000 |
| Octal (base 8) | 135770 |
| Hexadecimal (base 16) | BBF8 |
| Base 3 | 2110000020 |
| As time | 48120 seconds = 13 h 22 min 0 s |
Is 48120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48120 ÷ 2 = 24060) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48120 ÷ 3 = 16040) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48120 ÷ 4 = 12030) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48120 ÷ 5 = 9624) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48120 ÷ 6 = 8020) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (48120 ÷ 8 = 6015) | 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 | Yes (48120 ÷ 10 = 4812) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48120 ÷ 12 = 4010) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48120 a prime number?
No. 48120 = × 3 × 5 × 401, so it is divisible by 2.
What are the factors of 48120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 401, 802, 1203, 1604, 2005, 2406, 3208, 4010, 4812, 6015, 8020, 9624, 12030, 16040, 24060, 48120.
What is 48120 in binary?
1011101111111000 (hexadecimal BBF8, octal 135770).
What is the square root of 48120?
About 219.3627, exactly 2√12030.
Is 48120 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 48120?
48120 is a Harshad number: divisible by its digit sum 15.