The number 42900

Q: Is 42900 a prime number?

No. 42900 = 2^2 × 3 × 5^2 × 11 × 13, so it is divisible by 2.

42900 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 11 × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 15, 20, 22, 25, 26, 30 … 42900.

Number

Pick any whole number from 1 to 100,000.

42900 = 2^{2} \times 3 \times 5^{2} \times 11 \times 13

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How to work it out

1
What is special about 42900: a Harshad number: divisible by its digit sum 15.
2
42900 is composite. Its prime factorisation is
$42900 = 2^{2} \times 3 \times 5^{2} \times 11 \times 13$
3
The divisors add up to 145824; without 42900 itself that is 102924, so 42900 is abundant (102924 is more than 42900). Euler's totient φ(42900) = 9600 numbers up to 42900 share no factor with it.
4
The digits of 42900 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.

LaTeX source of the formulas on this page

\[ 42900 = 2^{2} \times 3 \times 5^{2} \times 11 \times 13 \]

42900 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	145824
Euler totient φ(n)	9600
Square	1840410000
Cube	78953589000000
Square root	207.123152 (= 10√429)
Digit sum / digital root	15 / 6
Collatz steps to 1	49
Scientific notation	4.29 × $10^{4}$

42900 in other forms

Form	Value
In words	forty-two thousand nine hundred
Binary (base 2)	1010011110010100
Octal (base 8)	123624
Hexadecimal (base 16)	A794
Base 3	2011211220
As time	42900 seconds = 11 h 55 min 0 s

Is 42900 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (42900 ÷ 2 = 21450)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (42900 ÷ 3 = 14300)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (42900 ÷ 4 = 10725)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (42900 ÷ 5 = 8580)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (42900 ÷ 6 = 7150)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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 (42900 ÷ 10 = 4290)	A number is divisible by 10 if the last digit is 0.
11	Yes (42900 ÷ 11 = 3900)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (42900 ÷ 12 = 3575)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 42900 a prime number?

No. 42900 = $2^{2}$ × 3 × $5^{2}$ × 11 × 13, so it is divisible by 2.

What are the factors of 42900?

1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 15, 20, 22, 25, 26, 30, 33, 39, 44, 50, 52, 55, 60, 65, 66, 75, 78, 100, 110, 130, 132, 143, 150, 156, 165, 195, 220, 260, 275, 286, 300, 325, 330, 390, 429, 550, 572, 650, 660, 715, 780, 825, 858, 975, 1100, 1300, 1430, 1650, 1716, 1950, 2145, 2860, 3300, 3575, 3900, 4290, 7150, 8580, 10725, 14300, 21450, 42900.

What is 42900 in binary?

1010011110010100 (hexadecimal A794, octal 123624).

What is the square root of 42900?

About 207.1232, exactly 10√429.

Is 42900 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 42900?

42900 is a Harshad number: divisible by its digit sum 15.