The number 48720
48720 is a composite number with 80 divisors. Its prime factorisation is × 3 × 5 × 7 × 29. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 48720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48720: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
48720 is composite. Its prime factorisation is
- 3
The divisors add up to 178560; without 48720 itself that is 129840, so 48720 is abundant (129840 is more than 48720). Euler's totient φ(48720) = 10752 numbers up to 48720 share no factor with it.
- 4
The digits of 48720 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48720 = 2^{4} \times 3 \times 5 \times 7 \times 29 \]48720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 178560 |
| Euler totient φ(n) | 10752 |
| Square | 2373638400 |
| Cube | 115643662848000 |
| Square root | 220.726075 (= 4√3045) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 39 |
| Scientific notation | 4.872 × |
48720 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand seven hundred and twenty |
| Binary (base 2) | 1011111001010000 |
| Octal (base 8) | 137120 |
| Hexadecimal (base 16) | BE50 |
| Base 3 | 2110211110 |
| As time | 48720 seconds = 13 h 32 min 0 s |
Is 48720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48720 ÷ 2 = 24360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48720 ÷ 3 = 16240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48720 ÷ 4 = 12180) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48720 ÷ 5 = 9744) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48720 ÷ 6 = 8120) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (48720 ÷ 7 = 6960) | 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 (48720 ÷ 8 = 6090) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (48720 ÷ 10 = 4872) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48720 ÷ 12 = 4060) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48720 a prime number?
No. 48720 = × 3 × 5 × 7 × 29, so it is divisible by 2.
What are the factors of 48720?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 29, 30, 35, 40, 42, 48, 56, 58, 60, 70, 80, 84, 87, 105, 112, 116, 120, 140, 145, 168, 174, 203, 210, 232, 240, 280, 290, 336, 348, 406, 420, 435, 464, 560, 580, 609, 696, 812, 840, 870, 1015, 1160, 1218, 1392, 1624, 1680, 1740, 2030, 2320, 2436, 3045, 3248, 3480, 4060, 4872, 6090, 6960, 8120, 9744, 12180, 16240, 24360, 48720.
What is 48720 in binary?
1011111001010000 (hexadecimal BE50, octal 137120).
What is the square root of 48720?
About 220.7261, exactly 4√3045.
Is 48720 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 48720?
48720 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.