The number 370
370 is an Armstrong number: each digit raised to the power 3 adds up to 370. Its prime factorisation is 2 × 5 × 37. Divisors (8): 1, 2, 5, 10, 37, 74, 185, 370.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 370: an Armstrong number: each digit raised to the power 3 adds up to 370; a Harshad number: divisible by its digit sum 10.
- 2
370 is composite. Its prime factorisation is
- 3
The divisors add up to 684; without 370 itself that is 314, so 370 is deficient (314 is less than 370). Euler's totient φ(370) = 144 numbers up to 370 share no factor with it.
- 4
The digits of 370 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.
LaTeX source of the formulas on this page
\[ 370 = 2 \times 5 \times 37 \]
370 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 684 |
| Euler totient φ(n) | 144 |
| Square | 136900 |
| Cube | 50653000 |
| Square root | 19.235384 |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 45 |
| Scientific notation | 3.7 × |
370 in other forms
| Form | Value |
|---|---|
| In words | three hundred and seventy |
| Roman numerals | CCCLXX |
| Binary (base 2) | 101110010 |
| Octal (base 8) | 562 |
| Hexadecimal (base 16) | 172 |
| Base 3 | 111201 |
| As time | 370 seconds = 6 min 10 s |
Is 370 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (370 ÷ 2 = 185) | 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 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (370 ÷ 5 = 74) | 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 6) | 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 2) | 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 | Yes (370 ÷ 10 = 37) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 370 a prime number?
No. 370 = 2 × 5 × 37, so it is divisible by 2.
What are the factors of 370?
1, 2, 5, 10, 37, 74, 185, 370.
What is 370 in binary?
101110010 (hexadecimal 172, octal 562).
What is the square root of 370?
About 19.2354.
What is 370 in Roman numerals?
CCCLXX.
Is 370 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 370?
370 is an Armstrong number: each digit raised to the power 3 adds up to 370; a Harshad number: divisible by its digit sum 10.