The number 420
420 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 7. Divisors (24): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35 … 420.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 420: a Harshad number: divisible by its digit sum 6.
- 2
420 is composite. Its prime factorisation is
- 3
The divisors add up to 1344; without 420 itself that is 924, so 420 is abundant (924 is more than 420). Euler's totient φ(420) = 96 numbers up to 420 share no factor with it.
- 4
The digits of 420 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 40 steps to reach 1.
LaTeX source of the formulas on this page
\[ 420 = 2^{2} \times 3 \times 5 \times 7 \]420 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 1344 |
| Euler totient φ(n) | 96 |
| Square | 176400 |
| Cube | 74088000 |
| Square root | 20.493902 (= 2√105) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 40 |
| Scientific notation | 4.2 × |
420 in other forms
| Form | Value |
|---|---|
| In words | four hundred and twenty |
| Roman numerals | CDXX |
| Binary (base 2) | 110100100 |
| Octal (base 8) | 644 |
| Hexadecimal (base 16) | 1A4 |
| Base 3 | 120120 |
| As time | 420 seconds = 7 min 0 s |
Is 420 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (420 ÷ 2 = 210) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (420 ÷ 3 = 140) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (420 ÷ 4 = 105) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (420 ÷ 5 = 84) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (420 ÷ 6 = 70) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (420 ÷ 7 = 60) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (420 ÷ 10 = 42) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (420 ÷ 12 = 35) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 420 a prime number?
No. 420 = × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 420?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420.
What is 420 in binary?
110100100 (hexadecimal 1A4, octal 644).
What is the square root of 420?
About 20.4939, exactly 2√105.
What is 420 in Roman numerals?
CDXX.
Is 420 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 420?
420 is a Harshad number: divisible by its digit sum 6.