The number 120
120 is a highly composite number: it has 16 divisors, more than any smaller number, 5! (5 factorial) and a triangular number: 1 + 2 + … + 15 = 120. Its prime factorisation is × 3 × 5. Divisors (16): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Pick any whole number from 1 to 100,000.
How to work it out
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What is special about 120: a highly composite number: it has 16 divisors, more than any smaller number; 5! (5 factorial); a triangular number: 1 + 2 + … + 15 = 120; a Harshad number: divisible by its digit sum 3.
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120 is composite. Its prime factorisation is
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The divisors add up to 360; without 120 itself that is 240, so 120 is abundant (240 is more than 120). Euler's totient φ(120) = 32 numbers up to 120 share no factor with it.
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The digits of 120 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 20 steps to reach 1.
LaTeX source of the formulas on this page
\[ 120 = 2^{3} \times 3 \times 5 \]120 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 360 |
| Euler totient φ(n) | 32 |
| Square | 14400 |
| Cube | 1728000 |
| Square root | 10.954451 (= 2√30) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 20 |
| Scientific notation | 1.2 × |
120 in other forms
| Form | Value |
|---|---|
| In words | one hundred and twenty |
| Roman numerals | CXX |
| Binary (base 2) | 1111000 |
| Octal (base 8) | 170 |
| Hexadecimal (base 16) | 78 |
| Base 3 | 11110 |
| As time | 120 seconds = 2 min 0 s |
Is 120 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (120 ÷ 2 = 60) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (120 ÷ 3 = 40) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (120 ÷ 4 = 30) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (120 ÷ 5 = 24) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (120 ÷ 6 = 20) | 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 (120 ÷ 8 = 15) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (120 ÷ 10 = 12) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (120 ÷ 12 = 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 120 a prime number?
No. 120 = × 3 × 5, so it is divisible by 2.
What are the factors of 120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
What is 120 in binary?
1111000 (hexadecimal 78, octal 170).
What is the square root of 120?
About 10.9545, exactly 2√30.
What is 120 in Roman numerals?
CXX.
Is 120 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 120?
120 is a highly composite number: it has 16 divisors, more than any smaller number; 5! (5 factorial); a triangular number: 1 + 2 + … + 15 = 120; a Harshad number: divisible by its digit sum 3.