The number 72996

Q: Is 72996 a prime number?

No. 72996 = 2^2 × 3 × 7 × 11 × 79, so it is divisible by 2.

72996 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 7 × 11 × 79. Divisors (48): 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66 … 72996.

Number

Pick any whole number from 1 to 100,000.

72996 = 2^{2} \times 3 \times 7 \times 11 \times 79

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How to work it out

1
What is special about 72996: a Harshad number: divisible by its digit sum 33.
2
72996 is composite. Its prime factorisation is
$72996 = 2^{2} \times 3 \times 7 \times 11 \times 79$
3
The divisors add up to 215040; without 72996 itself that is 142044, so 72996 is abundant (142044 is more than 72996). Euler's totient φ(72996) = 18720 numbers up to 72996 share no factor with it.
4
The digits of 72996 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.

LaTeX source of the formulas on this page

\[ 72996 = 2^{2} \times 3 \times 7 \times 11 \times 79 \]

72996 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	215040
Euler totient φ(n)	18720
Square	5328416016
Cube	388953055503936
Square root	270.177719 (= 2√18249)
Digit sum / digital root	33 / 6
Collatz steps to 1	143
Scientific notation	7.2996 × $10^{4}$

72996 in other forms

Form	Value
In words	seventy-two thousand nine hundred and ninety-six
Binary (base 2)	10001110100100100
Octal (base 8)	216444
Hexadecimal (base 16)	11D24
Base 3	10201010120
As time	72996 seconds = 20 h 16 min 36 s

Is 72996 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (72996 ÷ 2 = 36498)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (72996 ÷ 3 = 24332)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (72996 ÷ 4 = 18249)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 1)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (72996 ÷ 6 = 12166)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (72996 ÷ 7 = 10428)	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	No (remainder 6)	A number is divisible by 10 if the last digit is 0.
11	Yes (72996 ÷ 11 = 6636)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (72996 ÷ 12 = 6083)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 72996 a prime number?

No. 72996 = $2^{2}$ × 3 × 7 × 11 × 79, so it is divisible by 2.

What are the factors of 72996?

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 79, 84, 132, 154, 158, 231, 237, 308, 316, 462, 474, 553, 869, 924, 948, 1106, 1659, 1738, 2212, 2607, 3318, 3476, 5214, 6083, 6636, 10428, 12166, 18249, 24332, 36498, 72996.

What is 72996 in binary?

10001110100100100 (hexadecimal 11D24, octal 216444).

What is the square root of 72996?

About 270.1777, exactly 2√18249.

Is 72996 divisible by 3?

Yes. Its digits add up to 33, a multiple of 3.

What is special about the number 72996?

72996 is a Harshad number: divisible by its digit sum 33.