The number 89964

Q: Is 89964 a prime number?

No. 89964 = 2^2 × 3^3 × 7^2 × 17, so it is divisible by 2.

89964 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × $7^{2}$ × 17. Divisors (72): 1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 27, 28, 34, 36 … 89964.

Number

Pick any whole number from 1 to 100,000.

89964 = 2^{2} \times 3^{3} \times 7^{2} \times 17

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How to work it out

1
What is special about 89964: a Harshad number: divisible by its digit sum 36.
2
89964 is composite. Its prime factorisation is
$89964 = 2^{2} \times 3^{3} \times 7^{2} \times 17$
3
The divisors add up to 287280; without 89964 itself that is 197316, so 89964 is abundant (197316 is more than 89964). Euler's totient φ(89964) = 24192 numbers up to 89964 share no factor with it.
4
The digits of 89964 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 71 steps to reach 1.

LaTeX source of the formulas on this page

\[ 89964 = 2^{2} \times 3^{3} \times 7^{2} \times 17 \]

89964 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	287280
Euler totient φ(n)	24192
Square	8093521296
Cube	728125549873344
Square root	299.939994 (= 42√51)
Digit sum / digital root	36 / 9
Collatz steps to 1	71
Scientific notation	8.9964 × $10^{4}$

89964 in other forms

Form	Value
In words	eighty-nine thousand nine hundred and sixty-four
Binary (base 2)	10101111101101100
Octal (base 8)	257554
Hexadecimal (base 16)	15F6C
Base 3	11120102000
As time	89964 seconds = 24 h 59 min 24 s

Is 89964 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (89964 ÷ 2 = 44982)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (89964 ÷ 3 = 29988)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (89964 ÷ 4 = 22491)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (89964 ÷ 6 = 14994)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (89964 ÷ 7 = 12852)	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	Yes (89964 ÷ 9 = 9996)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 4)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (89964 ÷ 12 = 7497)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 89964 a prime number?

No. 89964 = $2^{2}$ × $3^{3}$ × $7^{2}$ × 17, so it is divisible by 2.

What are the factors of 89964?

1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 27, 28, 34, 36, 42, 49, 51, 54, 63, 68, 84, 98, 102, 108, 119, 126, 147, 153, 189, 196, 204, 238, 252, 294, 306, 357, 378, 441, 459, 476, 588, 612, 714, 756, 833, 882, 918, 1071, 1323, 1428, 1666, 1764, 1836, 2142, 2499, 2646, 3213, 3332, 4284, 4998, 5292, 6426, 7497, 9996, 12852, 14994, 22491, 29988, 44982, 89964.

What is 89964 in binary?

10101111101101100 (hexadecimal 15F6C, octal 257554).

What is the square root of 89964?

About 299.9400, exactly 42√51.

Is 89964 divisible by 3?

Yes. Its digits add up to 36, a multiple of 3.

What is special about the number 89964?

89964 is a Harshad number: divisible by its digit sum 36.