The number 77740

Q: Is 77740 a prime number?

No. 77740 = 2^2 × 5 × 13^2 × 23, so it is divisible by 2.

77740 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 5 × $13^{2}$ × 23. Divisors (36): 1, 2, 4, 5, 10, 13, 20, 23, 26, 46, 52, 65, 92, 115, 130, 169 … 77740.

Number

Pick any whole number from 1 to 100,000.

77740 = 2^{2} \times 5 \times 13^{2} \times 23

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How to work it out

1
77740 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
77740 is composite. Its prime factorisation is
$77740 = 2^{2} \times 5 \times 13^{2} \times 23$
3
The divisors add up to 184464; without 77740 itself that is 106724, so 77740 is abundant (106724 is more than 77740). Euler's totient φ(77740) = 27456 numbers up to 77740 share no factor with it.
4
The digits of 77740 add up to 25, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77740 = 2^{2} \times 5 \times 13^{2} \times 23 \]

77740 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	184464
Euler totient φ(n)	27456
Square	6043507600
Cube	469822280824000
Square root	278.818938 (= 26√115)
Digit sum / digital root	25 / 7
Collatz steps to 1	125
Scientific notation	7.774 × $10^{4}$

77740 in other forms

Form	Value
In words	seventy-seven thousand seven hundred and forty
Binary (base 2)	10010111110101100
Octal (base 8)	227654
Hexadecimal (base 16)	12FAC
Base 3	10221122021
As time	77740 seconds = 21 h 35 min 40 s

Is 77740 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77740 ÷ 2 = 38870)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 1)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77740 ÷ 4 = 19435)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (77740 ÷ 5 = 15548)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 4)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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 7)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (77740 ÷ 10 = 7774)	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	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77740 a prime number?

No. 77740 = $2^{2}$ × 5 × $13^{2}$ × 23, so it is divisible by 2.

What are the factors of 77740?

1, 2, 4, 5, 10, 13, 20, 23, 26, 46, 52, 65, 92, 115, 130, 169, 230, 260, 299, 338, 460, 598, 676, 845, 1196, 1495, 1690, 2990, 3380, 3887, 5980, 7774, 15548, 19435, 38870, 77740.

What is 77740 in binary?

10010111110101100 (hexadecimal 12FAC, octal 227654).

What is the square root of 77740?

About 278.8189, exactly 26√115.

Is 77740 divisible by 3?

No. Its digits add up to 25, which is not a multiple of 3.

What is special about the number 77740?

It is a composite number with 36 divisors.