The number 76176

Q: Is 76176 a prime number?

No. 76176 = 2^4 × 3^2 × 23^2, so it is divisible by 2.

76176 is a perfect square (276²). Its prime factorisation is $2^{4}$ × $3^{2}$ × $23^{2}$ . Divisors (45): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 36, 46, 48, 69 … 76176.

Number

Pick any whole number from 1 to 100,000.

76176 = 2^{4} \times 3^{2} \times 23^{2}

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 76176: a perfect square (276²).
2
76176 is composite. Its prime factorisation is
$76176 = 2^{4} \times 3^{2} \times 23^{2}$
3
The divisors add up to 222859; without 76176 itself that is 146683, so 76176 is abundant (146683 is more than 76176). Euler's totient φ(76176) = 24288 numbers up to 76176 share no factor with it.
4
The digits of 76176 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 37 steps to reach 1.

LaTeX source of the formulas on this page

\[ 76176 = 2^{4} \times 3^{2} \times 23^{2} \]

76176 at a glance

Property	Value
Type	composite
Number of divisors	45
Sum of divisors	222859
Euler totient φ(n)	24288
Square	5802782976
Cube	442032795979776
Square root	276
Digit sum / digital root	27 / 9
Collatz steps to 1	37
Scientific notation	7.6176 × $10^{4}$
Perfect power	$276^{2}$

76176 in other forms

Form	Value
In words	seventy-six thousand one hundred and seventy-six
Binary (base 2)	10010100110010000
Octal (base 8)	224620
Hexadecimal (base 16)	12990
Base 3	10212111100
As time	76176 seconds = 21 h 9 min 36 s

Is 76176 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (76176 ÷ 2 = 38088)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (76176 ÷ 3 = 25392)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (76176 ÷ 4 = 19044)	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 (76176 ÷ 6 = 12696)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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 (76176 ÷ 8 = 9522)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (76176 ÷ 9 = 8464)	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	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (76176 ÷ 12 = 6348)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 76176 a prime number?

No. 76176 = $2^{4}$ × $3^{2}$ × $23^{2}$ , so it is divisible by 2.

What are the factors of 76176?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 36, 46, 48, 69, 72, 92, 138, 144, 184, 207, 276, 368, 414, 529, 552, 828, 1058, 1104, 1587, 1656, 2116, 3174, 3312, 4232, 4761, 6348, 8464, 9522, 12696, 19044, 25392, 38088, 76176.

What is 76176 in binary?

10010100110010000 (hexadecimal 12990, octal 224620).

What is the square root of 76176?

276, because 276 × 276 = 76176.

Is 76176 divisible by 3?

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

What is special about the number 76176?

76176 is a perfect square (276²).