The number 42000

Q: Is 42000 a prime number?

No. 42000 = 2^4 × 3 × 5^3 × 7, so it is divisible by 2.

42000 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × 3 × $5^{3}$ × 7. Divisors (80): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 42000.

Number

Pick any whole number from 1 to 100,000.

42000 = 2^{4} \times 3 \times 5^{3} \times 7

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How to work it out

1
What is special about 42000: a Harshad number: divisible by its digit sum 6.
2
42000 is composite. Its prime factorisation is
$42000 = 2^{4} \times 3 \times 5^{3} \times 7$
3
The divisors add up to 154752; without 42000 itself that is 112752, so 42000 is abundant (112752 is more than 42000). Euler's totient φ(42000) = 9600 numbers up to 42000 share no factor with it.
4
The digits of 42000 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 31 steps to reach 1.

LaTeX source of the formulas on this page

\[ 42000 = 2^{4} \times 3 \times 5^{3} \times 7 \]

42000 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	154752
Euler totient φ(n)	9600
Square	1764000000
Cube	74088000000000
Square root	204.939015 (= 20√105)
Digit sum / digital root	6 / 6
Collatz steps to 1	31
Scientific notation	4.2 × $10^{4}$

42000 in other forms

Form	Value
In words	forty-two thousand
Binary (base 2)	1010010000010000
Octal (base 8)	122020
Hexadecimal (base 16)	A410
Base 3	2010121120
As time	42000 seconds = 11 h 40 min 0 s

Is 42000 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (42000 ÷ 2 = 21000)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (42000 ÷ 3 = 14000)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (42000 ÷ 4 = 10500)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (42000 ÷ 5 = 8400)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (42000 ÷ 6 = 7000)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (42000 ÷ 7 = 6000)	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 (42000 ÷ 8 = 5250)	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 (42000 ÷ 10 = 4200)	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 (42000 ÷ 12 = 3500)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 42000 a prime number?

No. 42000 = $2^{4}$ × 3 × $5^{3}$ × 7, so it is divisible by 2.

What are the factors of 42000?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000, 42000.

What is 42000 in binary?

1010010000010000 (hexadecimal A410, octal 122020).

What is the square root of 42000?

About 204.9390, exactly 20√105.

Is 42000 divisible by 3?

Yes. Its digits add up to 6, a multiple of 3.

What is special about the number 42000?

42000 is a Harshad number: divisible by its digit sum 6.