The number 37972
37972 is a composite number with 12 divisors. Its prime factorisation is × 11 × 863. Divisors (12): 1, 2, 4, 11, 22, 44, 863, 1726, 3452, 9493, 18986, 37972.
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How to work it out
- 1
What is special about 37972: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
37972 is composite. Its prime factorisation is
- 3
The divisors add up to 72576; without 37972 itself that is 34604, so 37972 is deficient (34604 is less than 37972). Euler's totient φ(37972) = 17240 numbers up to 37972 share no factor with it.
- 4
The digits of 37972 add up to 28, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37972 = 2^{2} \times 11 \times 863 \]37972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 72576 |
| Euler totient φ(n) | 17240 |
| Square | 1441872784 |
| Cube | 54750793354048 |
| Square root | 194.864055 (= 2√9493) |
| Digit sum / digital root | 28 / 1 |
| Collatz steps to 1 | 80 |
| Scientific notation | 3.7972 × |
37972 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and seventy-two |
| Binary (base 2) | 1001010001010100 |
| Octal (base 8) | 112124 |
| Hexadecimal (base 16) | 9454 |
| Base 3 | 1221002101 |
| As time | 37972 seconds = 10 h 32 min 52 s |
Is 37972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37972 ÷ 2 = 18986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37972 ÷ 4 = 9493) | 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 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 | No (remainder 1) | 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 (37972 ÷ 11 = 3452) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37972 a prime number?
No. 37972 = × 11 × 863, so it is divisible by 2.
What are the factors of 37972?
1, 2, 4, 11, 22, 44, 863, 1726, 3452, 9493, 18986, 37972.
What is 37972 in binary?
1001010001010100 (hexadecimal 9454, octal 112124).
What is the square root of 37972?
About 194.8641, exactly 2√9493.
Is 37972 divisible by 3?
No. Its digits add up to 28, which is not a multiple of 3.
What is special about the number 37972?
37972 is a happy number: repeatedly adding the squares of its digits reaches 1.