The number 77616

Q: Is 77616 a prime number?

No. 77616 = 2^4 × 3^2 × 7^2 × 11, so it is divisible by 2.

77616 is a composite number with 90 divisors. Its prime factorisation is $2^{4}$ × $3^{2}$ × $7^{2}$ × 11. Divisors (90): 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 21, 22, 24 … 77616.

Number

Pick any whole number from 1 to 100,000.

77616 = 2^{4} \times 3^{2} \times 7^{2} \times 11

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

How to work it out

1
77616 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
77616 is composite. Its prime factorisation is
$77616 = 2^{4} \times 3^{2} \times 7^{2} \times 11$
3
The divisors add up to 275652; without 77616 itself that is 198036, so 77616 is abundant (198036 is more than 77616). Euler's totient φ(77616) = 20160 numbers up to 77616 share no factor with it.
4
The digits of 77616 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 169 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77616 = 2^{4} \times 3^{2} \times 7^{2} \times 11 \]

77616 at a glance

Property	Value
Type	composite
Number of divisors	90
Sum of divisors	275652
Euler totient φ(n)	20160
Square	6024243456
Cube	467577680080896
Square root	278.596482 (= 84√11)
Digit sum / digital root	27 / 9
Collatz steps to 1	169
Scientific notation	7.7616 × $10^{4}$

77616 in other forms

Form	Value
In words	seventy-seven thousand six hundred and sixteen
Binary (base 2)	10010111100110000
Octal (base 8)	227460
Hexadecimal (base 16)	12F30
Base 3	10221110200
As time	77616 seconds = 21 h 33 min 36 s

Is 77616 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77616 ÷ 2 = 38808)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77616 ÷ 3 = 25872)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77616 ÷ 4 = 19404)	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 (77616 ÷ 6 = 12936)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (77616 ÷ 7 = 11088)	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 (77616 ÷ 8 = 9702)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (77616 ÷ 9 = 8624)	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	Yes (77616 ÷ 11 = 7056)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (77616 ÷ 12 = 6468)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77616 a prime number?

No. 77616 = $2^{4}$ × $3^{2}$ × $7^{2}$ × 11, so it is divisible by 2.

What are the factors of 77616?

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 21, 22, 24, 28, 33, 36, 42, 44, 48, 49, 56, 63, 66, 72, 77, 84, 88, 98, 99, 112, 126, 132, 144, 147, 154, 168, 176, 196, 198, 231, 252, 264, 294, 308, 336, 392, 396, 441, 462, 504, 528, 539, 588, 616, 693, 784, 792, 882, 924, 1008, 1078, 1176, 1232, 1386, 1584, 1617, 1764, 1848, 2156, 2352, 2772, 3234, 3528, 3696, 4312, 4851, 5544, 6468, 7056, 8624, 9702, 11088, 12936, 19404, 25872, 38808, 77616.

What is 77616 in binary?

10010111100110000 (hexadecimal 12F30, octal 227460).

What is the square root of 77616?

About 278.5965, exactly 84√11.

Is 77616 divisible by 3?

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

What is special about the number 77616?

It is a composite number with 90 divisors.