The number 72072

Q: Is 72072 a prime number?

No. 72072 = 2^3 × 3^2 × 7 × 11 × 13, so it is divisible by 2.

72072 is a composite number with 96 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × 7 × 11 × 13. Divisors (96): 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 18, 21, 22, 24 … 72072.

Number

Pick any whole number from 1 to 100,000.

72072 = 2^{3} \times 3^{2} \times 7 \times 11 \times 13

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How to work it out

1
What is special about 72072: a Harshad number: divisible by its digit sum 18.
2
72072 is composite. Its prime factorisation is
$72072 = 2^{3} \times 3^{2} \times 7 \times 11 \times 13$
3
The divisors add up to 262080; without 72072 itself that is 190008, so 72072 is abundant (190008 is more than 72072). Euler's totient φ(72072) = 17280 numbers up to 72072 share no factor with it.
4
The digits of 72072 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.

LaTeX source of the formulas on this page

\[ 72072 = 2^{3} \times 3^{2} \times 7 \times 11 \times 13 \]

72072 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	262080
Euler totient φ(n)	17280
Square	5194373184
Cube	374368864117248
Square root	268.462288 (= 6√2002)
Digit sum / digital root	18 / 9
Collatz steps to 1	42
Scientific notation	7.2072 × $10^{4}$

72072 in other forms

Form	Value
In words	seventy-two thousand and seventy-two
Binary (base 2)	10001100110001000
Octal (base 8)	214610
Hexadecimal (base 16)	11988
Base 3	10122212100
As time	72072 seconds = 20 h 1 min 12 s

Is 72072 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (72072 ÷ 2 = 36036)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (72072 ÷ 3 = 24024)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (72072 ÷ 4 = 18018)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 2)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (72072 ÷ 6 = 12012)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (72072 ÷ 7 = 10296)	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 (72072 ÷ 8 = 9009)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (72072 ÷ 9 = 8008)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 2)	A number is divisible by 10 if the last digit is 0.
11	Yes (72072 ÷ 11 = 6552)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (72072 ÷ 12 = 6006)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 72072 a prime number?

No. 72072 = $2^{3}$ × $3^{2}$ × 7 × 11 × 13, so it is divisible by 2.

What are the factors of 72072?

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 18, 21, 22, 24, 26, 28, 33, 36, 39, 42, 44, 52, 56, 63, 66, 72, 77, 78, 84, 88, 91, 99, 104, 117, 126, 132, 143, 154, 156, 168, 182, 198, 231, 234, 252, 264, 273, 286, 308, 312, 364, 396, 429, 462, 468, 504, 546, 572, 616, 693, 728, 792, 819, 858, 924, 936, 1001, 1092, 1144, 1287, 1386, 1638, 1716, 1848, 2002, 2184, 2574, 2772, 3003, 3276, 3432, 4004, 5148, 5544, 6006, 6552, 8008, 9009, 10296, 12012, 18018, 24024, 36036, 72072.

What is 72072 in binary?

10001100110001000 (hexadecimal 11988, octal 214610).

What is the square root of 72072?

About 268.4623, exactly 6√2002.

Is 72072 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 72072?

72072 is a Harshad number: divisible by its digit sum 18.