The number 31740

Q: Is 31740 a prime number?

No. 31740 = 2^2 × 3 × 5 × 23^2, so it is divisible by 2.

31740 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × $23^{2}$ . Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92 … 31740.

Number

Pick any whole number from 1 to 100,000.

31740 = 2^{2} \times 3 \times 5 \times 23^{2}

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How to work it out

1
What is special about 31740: a Harshad number: divisible by its digit sum 15.
2
31740 is composite. Its prime factorisation is
$31740 = 2^{2} \times 3 \times 5 \times 23^{2}$
3
The divisors add up to 92904; without 31740 itself that is 61164, so 31740 is abundant (61164 is more than 31740). Euler's totient φ(31740) = 8096 numbers up to 31740 share no factor with it.
4
The digits of 31740 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.

LaTeX source of the formulas on this page

\[ 31740 = 2^{2} \times 3 \times 5 \times 23^{2} \]

31740 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	92904
Euler totient φ(n)	8096
Square	1007427600
Cube	31975752024000
Square root	178.157234 (= 46√15)
Digit sum / digital root	15 / 6
Collatz steps to 1	129
Scientific notation	3.174 × $10^{4}$

31740 in other forms

Form	Value
In words	thirty-one thousand seven hundred and forty
Binary (base 2)	111101111111100
Octal (base 8)	75774
Hexadecimal (base 16)	7BFC
Base 3	1121112120
As time	31740 seconds = 8 h 49 min 0 s

Is 31740 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (31740 ÷ 2 = 15870)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (31740 ÷ 3 = 10580)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (31740 ÷ 4 = 7935)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (31740 ÷ 5 = 6348)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (31740 ÷ 6 = 5290)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (31740 ÷ 10 = 3174)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (31740 ÷ 12 = 2645)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 31740 a prime number?

No. 31740 = $2^{2}$ × 3 × 5 × $23^{2}$ , so it is divisible by 2.

What are the factors of 31740?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 529, 690, 1058, 1380, 1587, 2116, 2645, 3174, 5290, 6348, 7935, 10580, 15870, 31740.

What is 31740 in binary?

111101111111100 (hexadecimal 7BFC, octal 75774).

What is the square root of 31740?

About 178.1572, exactly 46√15.

Is 31740 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 31740?

31740 is a Harshad number: divisible by its digit sum 15.