The number 54972
54972 is a composite number with 24 divisors. Its prime factorisation is × × 509. Divisors (24): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 509, 1018, 1527, 2036 … 54972.
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How to work it out
- 1
What is special about 54972: a Harshad number: divisible by its digit sum 27.
- 2
54972 is composite. Its prime factorisation is
- 3
The divisors add up to 142800; without 54972 itself that is 87828, so 54972 is abundant (87828 is more than 54972). Euler's totient φ(54972) = 18288 numbers up to 54972 share no factor with it.
- 4
The digits of 54972 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 215 steps to reach 1.
LaTeX source of the formulas on this page
\[ 54972 = 2^{2} \times 3^{3} \times 509 \]54972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 142800 |
| Euler totient φ(n) | 18288 |
| Square | 3021920784 |
| Cube | 166121029338048 |
| Square root | 234.461084 (= 6√1527) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 215 |
| Scientific notation | 5.4972 × |
54972 in other forms
| Form | Value |
|---|---|
| In words | fifty-four thousand nine hundred and seventy-two |
| Binary (base 2) | 1101011010111100 |
| Octal (base 8) | 153274 |
| Hexadecimal (base 16) | D6BC |
| Base 3 | 2210102000 |
| As time | 54972 seconds = 15 h 16 min 12 s |
Is 54972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (54972 ÷ 2 = 27486) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (54972 ÷ 3 = 18324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (54972 ÷ 4 = 13743) | 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 (54972 ÷ 6 = 9162) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (54972 ÷ 9 = 6108) | 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 (54972 ÷ 12 = 4581) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 54972 a prime number?
No. 54972 = × × 509, so it is divisible by 2.
What are the factors of 54972?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108, 509, 1018, 1527, 2036, 3054, 4581, 6108, 9162, 13743, 18324, 27486, 54972.
What is 54972 in binary?
1101011010111100 (hexadecimal D6BC, octal 153274).
What is the square root of 54972?
About 234.4611, exactly 6√1527.
Is 54972 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 54972?
54972 is a Harshad number: divisible by its digit sum 27.