The number 65472
65472 is a composite number with 56 divisors. Its prime factorisation is × 3 × 11 × 31. Divisors (56): 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 31, 32, 33, 44, 48 … 65472.
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How to work it out
- 1
What is special about 65472: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.
- 2
65472 is composite. Its prime factorisation is
- 3
The divisors add up to 195072; without 65472 itself that is 129600, so 65472 is abundant (129600 is more than 65472). Euler's totient φ(65472) = 19200 numbers up to 65472 share no factor with it.
- 4
The digits of 65472 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 65472 = 2^{6} \times 3 \times 11 \times 31 \]65472 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 195072 |
| Euler totient φ(n) | 19200 |
| Square | 4286582784 |
| Cube | 280651148034048 |
| Square root | 255.874969 (= 8√1023) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 68 |
| Scientific notation | 6.5472 × |
65472 in other forms
| Form | Value |
|---|---|
| In words | sixty-five thousand four hundred and seventy-two |
| Binary (base 2) | 1111111111000000 |
| Octal (base 8) | 177700 |
| Hexadecimal (base 16) | FFC0 |
| Base 3 | 10022210220 |
| As time | 65472 seconds = 18 h 11 min 12 s |
Is 65472 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (65472 ÷ 2 = 32736) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (65472 ÷ 3 = 21824) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (65472 ÷ 4 = 16368) | 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 (65472 ÷ 6 = 10912) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (65472 ÷ 8 = 8184) | 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 | Yes (65472 ÷ 11 = 5952) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (65472 ÷ 12 = 5456) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 65472 a prime number?
No. 65472 = × 3 × 11 × 31, so it is divisible by 2.
What are the factors of 65472?
1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 31, 32, 33, 44, 48, 62, 64, 66, 88, 93, 96, 124, 132, 176, 186, 192, 248, 264, 341, 352, 372, 496, 528, 682, 704, 744, 992, 1023, 1056, 1364, 1488, 1984, 2046, 2112, 2728, 2976, 4092, 5456, 5952, 8184, 10912, 16368, 21824, 32736, 65472.
What is 65472 in binary?
1111111111000000 (hexadecimal FFC0, octal 177700).
What is the square root of 65472?
About 255.8750, exactly 8√1023.
Is 65472 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 65472?
65472 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 24.