The number 23100

Q: Is 23100 a prime number?

No. 23100 = 2^2 × 3 × 5^2 × 7 × 11, so it is divisible by 2.

23100 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 7 × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 25 … 23100.

Number

Pick any whole number from 1 to 100,000.

23100 = 2^{2} \times 3 \times 5^{2} \times 7 \times 11

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 23100: a Harshad number: divisible by its digit sum 6.
2
23100 is composite. Its prime factorisation is
$23100 = 2^{2} \times 3 \times 5^{2} \times 7 \times 11$
3
The divisors add up to 83328; without 23100 itself that is 60228, so 23100 is abundant (60228 is more than 23100). Euler's totient φ(23100) = 4800 numbers up to 23100 share no factor with it.
4
The digits of 23100 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 131 steps to reach 1.

LaTeX source of the formulas on this page

\[ 23100 = 2^{2} \times 3 \times 5^{2} \times 7 \times 11 \]

23100 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	83328
Euler totient φ(n)	4800
Square	533610000
Cube	12326391000000
Square root	151.986842 (= 10√231)
Digit sum / digital root	6 / 6
Collatz steps to 1	131
Scientific notation	2.31 × $10^{4}$

23100 in other forms

Form	Value
In words	twenty-three thousand one hundred
Binary (base 2)	101101000111100
Octal (base 8)	55074
Hexadecimal (base 16)	5A3C
Base 3	1011200120
As time	23100 seconds = 6 h 25 min 0 s

Is 23100 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (23100 ÷ 2 = 11550)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (23100 ÷ 3 = 7700)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (23100 ÷ 4 = 5775)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (23100 ÷ 5 = 4620)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (23100 ÷ 6 = 3850)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (23100 ÷ 7 = 3300)	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 (23100 ÷ 10 = 2310)	A number is divisible by 10 if the last digit is 0.
11	Yes (23100 ÷ 11 = 2100)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (23100 ÷ 12 = 1925)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 23100 a prime number?

No. 23100 = $2^{2}$ × 3 × $5^{2}$ × 7 × 11, so it is divisible by 2.

What are the factors of 23100?

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 25, 28, 30, 33, 35, 42, 44, 50, 55, 60, 66, 70, 75, 77, 84, 100, 105, 110, 132, 140, 150, 154, 165, 175, 210, 220, 231, 275, 300, 308, 330, 350, 385, 420, 462, 525, 550, 660, 700, 770, 825, 924, 1050, 1100, 1155, 1540, 1650, 1925, 2100, 2310, 3300, 3850, 4620, 5775, 7700, 11550, 23100.

What is 23100 in binary?

101101000111100 (hexadecimal 5A3C, octal 55074).

What is the square root of 23100?

About 151.9868, exactly 10√231.

Is 23100 divisible by 3?

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

What is special about the number 23100?

23100 is a Harshad number: divisible by its digit sum 6.