The number 77520

Q: Is 77520 a prime number?

No. 77520 = 2^4 × 3 × 5 × 17 × 19, so it is divisible by 2.

77520 is a composite number with 80 divisors. Its prime factorisation is $2^{4}$ × 3 × 5 × 17 × 19. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 19, 20, 24, 30 … 77520.

Number

Pick any whole number from 1 to 100,000.

77520 = 2^{4} \times 3 \times 5 \times 17 \times 19

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How to work it out

1
77520 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
77520 is composite. Its prime factorisation is
$77520 = 2^{4} \times 3 \times 5 \times 17 \times 19$
3
The divisors add up to 267840; without 77520 itself that is 190320, so 77520 is abundant (190320 is more than 77520). Euler's totient φ(77520) = 18432 numbers up to 77520 share no factor with it.
4
The digits of 77520 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77520 = 2^{4} \times 3 \times 5 \times 17 \times 19 \]

77520 at a glance

Property	Value
Type	composite
Number of divisors	80
Sum of divisors	267840
Euler totient φ(n)	18432
Square	6009350400
Cube	465844843008000
Square root	278.424137 (= 4√4845)
Digit sum / digital root	21 / 3
Collatz steps to 1	76
Scientific notation	7.752 × $10^{4}$

77520 in other forms

Form	Value
In words	seventy-seven thousand five hundred and twenty
Binary (base 2)	10010111011010000
Octal (base 8)	227320
Hexadecimal (base 16)	12ED0
Base 3	10221100010
As time	77520 seconds = 21 h 32 min 0 s

Is 77520 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77520 ÷ 2 = 38760)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77520 ÷ 3 = 25840)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77520 ÷ 4 = 19380)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (77520 ÷ 5 = 15504)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (77520 ÷ 6 = 12920)	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 (77520 ÷ 8 = 9690)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (77520 ÷ 10 = 7752)	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 (77520 ÷ 12 = 6460)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77520 a prime number?

No. 77520 = $2^{4}$ × 3 × 5 × 17 × 19, so it is divisible by 2.

What are the factors of 77520?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 19, 20, 24, 30, 34, 38, 40, 48, 51, 57, 60, 68, 76, 80, 85, 95, 102, 114, 120, 136, 152, 170, 190, 204, 228, 240, 255, 272, 285, 304, 323, 340, 380, 408, 456, 510, 570, 646, 680, 760, 816, 912, 969, 1020, 1140, 1292, 1360, 1520, 1615, 1938, 2040, 2280, 2584, 3230, 3876, 4080, 4560, 4845, 5168, 6460, 7752, 9690, 12920, 15504, 19380, 25840, 38760, 77520.

What is 77520 in binary?

10010111011010000 (hexadecimal 12ED0, octal 227320).

What is the square root of 77520?

About 278.4241, exactly 4√4845.

Is 77520 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 77520?

It is a composite number with 80 divisors.