The number 77175

Q: Is 77175 a prime number?

No. 77175 = 3^2 × 5^2 × 7^3, so it is divisible by 3.

77175 is a composite number with 36 divisors. Its prime factorisation is $3^{2}$ × $5^{2}$ × $7^{3}$ . Divisors (36): 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 49, 63, 75, 105, 147, 175 … 77175.

Number

Pick any whole number from 1 to 100,000.

77175 = 3^{2} \times 5^{2} \times 7^{3}

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

How to work it out

1
77175 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
77175 is composite. Its prime factorisation is
$77175 = 3^{2} \times 5^{2} \times 7^{3}$
3
The divisors add up to 161200; without 77175 itself that is 84025, so 77175 is abundant (84025 is more than 77175). Euler's totient φ(77175) = 35280 numbers up to 77175 share no factor with it.
4
The digits of 77175 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 125 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77175 = 3^{2} \times 5^{2} \times 7^{3} \]

77175 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	161200
Euler totient φ(n)	35280
Square	5955980625
Cube	459652804734375
Square root	277.803888 (= 105√7)
Digit sum / digital root	27 / 9
Collatz steps to 1	125
Scientific notation	7.7175 × $10^{4}$

77175 in other forms

Form	Value
In words	seventy-seven thousand one hundred and seventy-five
Binary (base 2)	10010110101110111
Octal (base 8)	226567
Hexadecimal (base 16)	12D77
Base 3	10220212100
As time	77175 seconds = 21 h 26 min 15 s

Is 77175 divisible by 2 to 12?

Divisor	Answer	Rule
2	No (remainder 1)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77175 ÷ 3 = 25725)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	No (remainder 3)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (77175 ÷ 5 = 15435)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 3)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (77175 ÷ 7 = 11025)	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 7)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (77175 ÷ 9 = 8575)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 5)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 3)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77175 a prime number?

No. 77175 = $3^{2}$ × $5^{2}$ × $7^{3}$ , so it is divisible by 3.

What are the factors of 77175?

1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 49, 63, 75, 105, 147, 175, 225, 245, 315, 343, 441, 525, 735, 1029, 1225, 1575, 1715, 2205, 3087, 3675, 5145, 8575, 11025, 15435, 25725, 77175.

What is 77175 in binary?

10010110101110111 (hexadecimal 12D77, octal 226567).

What is the square root of 77175?

About 277.8039, exactly 105√7.

Is 77175 divisible by 3?

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

What is special about the number 77175?

It is a composite number with 36 divisors.