The number 31164

Q: Is 31164 a prime number?

No. 31164 = 2^2 × 3 × 7^2 × 53, so it is divisible by 2.

31164 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 3 × $7^{2}$ × 53. Divisors (36): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 53, 84, 98, 106 … 31164.

Number

Pick any whole number from 1 to 100,000.

31164 = 2^{2} \times 3 \times 7^{2} \times 53

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How to work it out

1
31164 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
31164 is composite. Its prime factorisation is
$31164 = 2^{2} \times 3 \times 7^{2} \times 53$
3
The divisors add up to 86184; without 31164 itself that is 55020, so 31164 is abundant (55020 is more than 31164). Euler's totient φ(31164) = 8736 numbers up to 31164 share no factor with it.
4
The digits of 31164 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 72 steps to reach 1.

LaTeX source of the formulas on this page

\[ 31164 = 2^{2} \times 3 \times 7^{2} \times 53 \]

31164 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	86184
Euler totient φ(n)	8736
Square	971194896
Cube	30266317738944
Square root	176.533283 (= 14√159)
Digit sum / digital root	15 / 6
Collatz steps to 1	72
Scientific notation	3.1164 × $10^{4}$

31164 in other forms

Form	Value
In words	thirty-one thousand one hundred and sixty-four
Binary (base 2)	111100110111100
Octal (base 8)	74674
Hexadecimal (base 16)	79BC
Base 3	1120202020
As time	31164 seconds = 8 h 39 min 24 s

Is 31164 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (31164 ÷ 2 = 15582)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (31164 ÷ 3 = 10388)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (31164 ÷ 4 = 7791)	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 (31164 ÷ 6 = 5194)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (31164 ÷ 7 = 4452)	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 4)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (31164 ÷ 12 = 2597)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 31164 a prime number?

No. 31164 = $2^{2}$ × 3 × $7^{2}$ × 53, so it is divisible by 2.

What are the factors of 31164?

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 53, 84, 98, 106, 147, 159, 196, 212, 294, 318, 371, 588, 636, 742, 1113, 1484, 2226, 2597, 4452, 5194, 7791, 10388, 15582, 31164.

What is 31164 in binary?

111100110111100 (hexadecimal 79BC, octal 74674).

What is the square root of 31164?

About 176.5333, exactly 14√159.

Is 31164 divisible by 3?

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

What is special about the number 31164?

It is a composite number with 36 divisors.