The number 76752

Q: Is 76752 a prime number?

No. 76752 = 2^4 × 3^2 × 13 × 41, so it is divisible by 2.

76752 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × $3^{2}$ × 13 × 41. Divisors (60): 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 41 … 76752.

Number

Pick any whole number from 1 to 100,000.

76752 = 2^{4} \times 3^{2} \times 13 \times 41

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How to work it out

1
76752 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
76752 is composite. Its prime factorisation is
$76752 = 2^{4} \times 3^{2} \times 13 \times 41$
3
The divisors add up to 236964; without 76752 itself that is 160212, so 76752 is abundant (160212 is more than 76752). Euler's totient φ(76752) = 23040 numbers up to 76752 share no factor with it.
4
The digits of 76752 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 76 steps to reach 1.

LaTeX source of the formulas on this page

\[ 76752 = 2^{4} \times 3^{2} \times 13 \times 41 \]

76752 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	236964
Euler totient φ(n)	23040
Square	5890869504
Cube	452136016171008
Square root	277.041513 (= 12√533)
Digit sum / digital root	27 / 9
Collatz steps to 1	76
Scientific notation	7.6752 × $10^{4}$

76752 in other forms

Form	Value
In words	seventy-six thousand seven hundred and fifty-two
Binary (base 2)	10010101111010000
Octal (base 8)	225720
Hexadecimal (base 16)	12BD0
Base 3	10220021200
As time	76752 seconds = 21 h 19 min 12 s

Is 76752 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (76752 ÷ 2 = 38376)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (76752 ÷ 3 = 25584)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (76752 ÷ 4 = 19188)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 2)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (76752 ÷ 6 = 12792)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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 (76752 ÷ 8 = 9594)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (76752 ÷ 9 = 8528)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 2)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (76752 ÷ 12 = 6396)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 76752 a prime number?

No. 76752 = $2^{4}$ × $3^{2}$ × 13 × 41, so it is divisible by 2.

What are the factors of 76752?

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 41, 48, 52, 72, 78, 82, 104, 117, 123, 144, 156, 164, 208, 234, 246, 312, 328, 369, 468, 492, 533, 624, 656, 738, 936, 984, 1066, 1476, 1599, 1872, 1968, 2132, 2952, 3198, 4264, 4797, 5904, 6396, 8528, 9594, 12792, 19188, 25584, 38376, 76752.

What is 76752 in binary?

10010101111010000 (hexadecimal 12BD0, octal 225720).

What is the square root of 76752?

About 277.0415, exactly 12√533.

Is 76752 divisible by 3?

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

What is special about the number 76752?

It is a composite number with 60 divisors.