The number 4200
4200 is a composite number with 48 divisors. Its prime factorisation is × 3 × × 7. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25 … 4200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4200: a Harshad number: divisible by its digit sum 6.
- 2
4200 is composite. Its prime factorisation is
- 3
The divisors add up to 14880; without 4200 itself that is 10680, so 4200 is abundant (10680 is more than 4200). Euler's totient φ(4200) = 960 numbers up to 4200 share no factor with it.
- 4
The digits of 4200 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 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4200 = 2^{3} \times 3 \times 5^{2} \times 7 \]4200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 14880 |
| Euler totient φ(n) | 960 |
| Square | 17640000 |
| Cube | 74088000000 |
| Square root | 64.807407 (= 10√42) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 33 |
| Scientific notation | 4.2 × |
4200 in other forms
| Form | Value |
|---|---|
| In words | four thousand two hundred |
| Binary (base 2) | 1000001101000 |
| Octal (base 8) | 10150 |
| Hexadecimal (base 16) | 1068 |
| Base 3 | 12202120 |
| As time | 4200 seconds = 1 h 10 min 0 s |
Is 4200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4200 ÷ 2 = 2100) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4200 ÷ 3 = 1400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4200 ÷ 4 = 1050) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4200 ÷ 5 = 840) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (4200 ÷ 6 = 700) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (4200 ÷ 7 = 600) | 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 (4200 ÷ 8 = 525) | 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 (4200 ÷ 10 = 420) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (4200 ÷ 12 = 350) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4200 a prime number?
No. 4200 = × 3 × × 7, so it is divisible by 2.
What are the factors of 4200?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 140, 150, 168, 175, 200, 210, 280, 300, 350, 420, 525, 600, 700, 840, 1050, 1400, 2100, 4200.
What is 4200 in binary?
1000001101000 (hexadecimal 1068, octal 10150).
What is the square root of 4200?
About 64.8074, exactly 10√42.
Is 4200 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 4200?
4200 is a Harshad number: divisible by its digit sum 6.