The number 5472
5472 is a composite number with 36 divisors. Its prime factorisation is × × 19. Divisors (36): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 32, 36, 38, 48 … 5472.
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How to work it out
- 1
What is special about 5472: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
5472 is composite. Its prime factorisation is
- 3
The divisors add up to 16380; without 5472 itself that is 10908, so 5472 is abundant (10908 is more than 5472). Euler's totient φ(5472) = 1728 numbers up to 5472 share no factor with it.
- 4
The digits of 5472 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5472 = 2^{5} \times 3^{2} \times 19 \]5472 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 16380 |
| Euler totient φ(n) | 1728 |
| Square | 29942784 |
| Cube | 163846914048 |
| Square root | 73.972968 (= 12√38) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 129 |
| Scientific notation | 5.472 × |
5472 in other forms
| Form | Value |
|---|---|
| In words | five thousand four hundred and seventy-two |
| Binary (base 2) | 1010101100000 |
| Octal (base 8) | 12540 |
| Hexadecimal (base 16) | 1560 |
| Base 3 | 21111200 |
| As time | 5472 seconds = 1 h 31 min 12 s |
Is 5472 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5472 ÷ 2 = 2736) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (5472 ÷ 3 = 1824) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (5472 ÷ 4 = 1368) | 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 (5472 ÷ 6 = 912) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (5472 ÷ 8 = 684) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (5472 ÷ 9 = 608) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (5472 ÷ 12 = 456) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5472 a prime number?
No. 5472 = × × 19, so it is divisible by 2.
What are the factors of 5472?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 32, 36, 38, 48, 57, 72, 76, 96, 114, 144, 152, 171, 228, 288, 304, 342, 456, 608, 684, 912, 1368, 1824, 2736, 5472.
What is 5472 in binary?
1010101100000 (hexadecimal 1560, octal 12540).
What is the square root of 5472?
About 73.9730, exactly 12√38.
Is 5472 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 5472?
5472 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.