The number 37180

Q: Is 37180 a prime number?

No. 37180 = 2^2 × 5 × 11 × 13^2, so it is divisible by 2.

37180 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 5 × 11 × $13^{2}$ . Divisors (36): 1, 2, 4, 5, 10, 11, 13, 20, 22, 26, 44, 52, 55, 65, 110, 130 … 37180.

Number

Pick any whole number from 1 to 100,000.

37180 = 2^{2} \times 5 \times 11 \times 13^{2}

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

How to work it out

1
37180 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
37180 is composite. Its prime factorisation is
$37180 = 2^{2} \times 5 \times 11 \times 13^{2}$
3
The divisors add up to 92232; without 37180 itself that is 55052, so 37180 is abundant (55052 is more than 37180). Euler's totient φ(37180) = 12480 numbers up to 37180 share no factor with it.
4
The digits of 37180 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.

LaTeX source of the formulas on this page

\[ 37180 = 2^{2} \times 5 \times 11 \times 13^{2} \]

37180 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	92232
Euler totient φ(n)	12480
Square	1382352400
Cube	51395862232000
Square root	192.821161 (= 26√55)
Digit sum / digital root	19 / 1
Collatz steps to 1	62
Scientific notation	3.718 × $10^{4}$

37180 in other forms

Form	Value
In words	thirty-seven thousand one hundred and eighty
Binary (base 2)	1001000100111100
Octal (base 8)	110474
Hexadecimal (base 16)	913C
Base 3	1220000001
As time	37180 seconds = 10 h 19 min 40 s

Is 37180 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (37180 ÷ 2 = 18590)	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 (37180 ÷ 4 = 9295)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (37180 ÷ 5 = 7436)	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 3)	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 1)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (37180 ÷ 10 = 3718)	A number is divisible by 10 if the last digit is 0.
11	Yes (37180 ÷ 11 = 3380)	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 37180 a prime number?

No. 37180 = $2^{2}$ × 5 × 11 × $13^{2}$ , so it is divisible by 2.

What are the factors of 37180?

1, 2, 4, 5, 10, 11, 13, 20, 22, 26, 44, 52, 55, 65, 110, 130, 143, 169, 220, 260, 286, 338, 572, 676, 715, 845, 1430, 1690, 1859, 2860, 3380, 3718, 7436, 9295, 18590, 37180.

What is 37180 in binary?

1001000100111100 (hexadecimal 913C, octal 110474).

What is the square root of 37180?

About 192.8212, exactly 26√55.

Is 37180 divisible by 3?

No. Its digits add up to 19, which is not a multiple of 3.

What is special about the number 37180?

It is a composite number with 36 divisors.