The number 33124

Q: Is 33124 a prime number?

No. 33124 = 2^2 × 7^2 × 13^2, so it is divisible by 2.

33124 is a perfect square (182²). Its prime factorisation is $2^{2}$ × $7^{2}$ × $13^{2}$ . Divisors (27): 1, 2, 4, 7, 13, 14, 26, 28, 49, 52, 91, 98, 169, 182, 196, 338 … 33124.

Number

Pick any whole number from 1 to 100,000.

33124 = 2^{2} \times 7^{2} \times 13^{2}

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How to work it out

1
What is special about 33124: a perfect square (182²); a Harshad number: divisible by its digit sum 13.
2
33124 is composite. Its prime factorisation is
$33124 = 2^{2} \times 7^{2} \times 13^{2}$
3
The divisors add up to 73017; without 33124 itself that is 39893, so 33124 is abundant (39893 is more than 33124). Euler's totient φ(33124) = 13104 numbers up to 33124 share no factor with it.
4
The digits of 33124 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 160 steps to reach 1.

LaTeX source of the formulas on this page

\[ 33124 = 2^{2} \times 7^{2} \times 13^{2} \]

33124 at a glance

Property	Value
Type	composite
Number of divisors	27
Sum of divisors	73017
Euler totient φ(n)	13104
Square	1097199376
Cube	36343632130624
Square root	182
Digit sum / digital root	13 / 4
Collatz steps to 1	160
Scientific notation	3.3124 × $10^{4}$
Perfect power	$182^{2}$

33124 in other forms

Form	Value
In words	thirty-three thousand one hundred and twenty-four
Binary (base 2)	1000000101100100
Octal (base 8)	100544
Hexadecimal (base 16)	8164
Base 3	1200102211
As time	33124 seconds = 9 h 12 min 4 s

Is 33124 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (33124 ÷ 2 = 16562)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 1)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (33124 ÷ 4 = 8281)	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	No (remainder 4)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (33124 ÷ 7 = 4732)	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 4)	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 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 33124 a prime number?

No. 33124 = $2^{2}$ × $7^{2}$ × $13^{2}$ , so it is divisible by 2.

What are the factors of 33124?

1, 2, 4, 7, 13, 14, 26, 28, 49, 52, 91, 98, 169, 182, 196, 338, 364, 637, 676, 1183, 1274, 2366, 2548, 4732, 8281, 16562, 33124.

What is 33124 in binary?

1000000101100100 (hexadecimal 8164, octal 100544).

What is the square root of 33124?

182, because 182 × 182 = 33124.

Is 33124 divisible by 3?

No. Its digits add up to 13, which is not a multiple of 3.

What is special about the number 33124?

33124 is a perfect square (182²); a Harshad number: divisible by its digit sum 13.