The number 77924

Q: Is 77924 a prime number?

No. 77924 = 2^2 × 7 × 11^2 × 23, so it is divisible by 2.

77924 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 7 × $11^{2}$ × 23. Divisors (36): 1, 2, 4, 7, 11, 14, 22, 23, 28, 44, 46, 77, 92, 121, 154, 161 … 77924.

Number

Pick any whole number from 1 to 100,000.

77924 = 2^{2} \times 7 \times 11^{2} \times 23

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How to work it out

1
77924 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
77924 is composite. Its prime factorisation is
$77924 = 2^{2} \times 7 \times 11^{2} \times 23$
3
The divisors add up to 178752; without 77924 itself that is 100828, so 77924 is abundant (100828 is more than 77924). Euler's totient φ(77924) = 29040 numbers up to 77924 share no factor with it.
4
The digits of 77924 add up to 29, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 200 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77924 = 2^{2} \times 7 \times 11^{2} \times 23 \]

77924 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	178752
Euler totient φ(n)	29040
Square	6072149776
Cube	473166199145024
Square root	279.148706 (= 22√161)
Digit sum / digital root	29 / 2
Collatz steps to 1	200
Scientific notation	7.7924 × $10^{4}$

77924 in other forms

Form	Value
In words	seventy-seven thousand nine hundred and twenty-four
Binary (base 2)	10011000001100100
Octal (base 8)	230144
Hexadecimal (base 16)	13064
Base 3	10221220002
As time	77924 seconds = 21 h 38 min 44 s

Is 77924 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77924 ÷ 2 = 38962)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77924 ÷ 4 = 19481)	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 2)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (77924 ÷ 7 = 11132)	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 2)	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	Yes (77924 ÷ 11 = 7084)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77924 a prime number?

No. 77924 = $2^{2}$ × 7 × $11^{2}$ × 23, so it is divisible by 2.

What are the factors of 77924?

1, 2, 4, 7, 11, 14, 22, 23, 28, 44, 46, 77, 92, 121, 154, 161, 242, 253, 308, 322, 484, 506, 644, 847, 1012, 1694, 1771, 2783, 3388, 3542, 5566, 7084, 11132, 19481, 38962, 77924.

What is 77924 in binary?

10011000001100100 (hexadecimal 13064, octal 230144).

What is the square root of 77924?

About 279.1487, exactly 22√161.

Is 77924 divisible by 3?

No. Its digits add up to 29, which is not a multiple of 3.

What is special about the number 77924?

It is a composite number with 36 divisors.