The number 74088

Q: Is 74088 a prime number?

No. 74088 = 2^3 × 3^3 × 7^3, so it is divisible by 2.

Q: What is special about the number 74088?

74088 is a perfect cube (42^3); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.

74088 is a perfect cube ( $42^{3}$ ). Its prime factorisation is $2^{3}$ × $3^{3}$ × $7^{3}$ . Divisors (64): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36 … 74088.

Number

Pick any whole number from 1 to 100,000.

74088 = 2^{3} \times 3^{3} \times 7^{3}

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How to work it out

1
What is special about 74088: a perfect cube ( $42^{3}$ ); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
2
74088 is composite. Its prime factorisation is
$74088 = 2^{3} \times 3^{3} \times 7^{3}$
3
The divisors add up to 240000; without 74088 itself that is 165912, so 74088 is abundant (165912 is more than 74088). Euler's totient φ(74088) = 21168 numbers up to 74088 share no factor with it.
4
The digits of 74088 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 112 steps to reach 1.

LaTeX source of the formulas on this page

\[ 74088 = 2^{3} \times 3^{3} \times 7^{3} \]

74088 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	240000
Euler totient φ(n)	21168
Square	5489031744
Cube	406671383849472
Square root	272.191109 (= 42√42)
Digit sum / digital root	27 / 9
Collatz steps to 1	112
Scientific notation	7.4088 × $10^{4}$
Perfect power	$42^{3}$

74088 in other forms

Form	Value
In words	seventy-four thousand and eighty-eight
Binary (base 2)	10010000101101000
Octal (base 8)	220550
Hexadecimal (base 16)	12168
Base 3	10202122000
As time	74088 seconds = 20 h 34 min 48 s

Is 74088 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (74088 ÷ 2 = 37044)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (74088 ÷ 3 = 24696)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (74088 ÷ 4 = 18522)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (74088 ÷ 6 = 12348)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (74088 ÷ 7 = 10584)	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 (74088 ÷ 8 = 9261)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (74088 ÷ 9 = 8232)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 8)	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	Yes (74088 ÷ 12 = 6174)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 74088 a prime number?

No. 74088 = $2^{3}$ × $3^{3}$ × $7^{3}$ , so it is divisible by 2.

What are the factors of 74088?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 49, 54, 56, 63, 72, 84, 98, 108, 126, 147, 168, 189, 196, 216, 252, 294, 343, 378, 392, 441, 504, 588, 686, 756, 882, 1029, 1176, 1323, 1372, 1512, 1764, 2058, 2646, 2744, 3087, 3528, 4116, 5292, 6174, 8232, 9261, 10584, 12348, 18522, 24696, 37044, 74088.

What is 74088 in binary?

10010000101101000 (hexadecimal 12168, octal 220550).

What is the square root of 74088?

About 272.1911, exactly 42√42.

Is 74088 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 74088?

74088 is a perfect cube ( $42^{3}$ ); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.