The number 31500

Q: Is 31500 a prime number?

No. 31500 = 2^2 × 3^2 × 5^3 × 7, so it is divisible by 2.

31500 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × $5^{3}$ × 7. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25 … 31500.

Number

Pick any whole number from 1 to 100,000.

31500 = 2^{2} \times 3^{2} \times 5^{3} \times 7

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How to work it out

1
What is special about 31500: a Harshad number: divisible by its digit sum 9.
2
31500 is composite. Its prime factorisation is
$31500 = 2^{2} \times 3^{2} \times 5^{3} \times 7$
3
The divisors add up to 113568; without 31500 itself that is 82068, so 31500 is abundant (82068 is more than 31500). Euler's totient φ(31500) = 7200 numbers up to 31500 share no factor with it.
4
The digits of 31500 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 129 steps to reach 1.

LaTeX source of the formulas on this page

\[ 31500 = 2^{2} \times 3^{2} \times 5^{3} \times 7 \]

31500 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	113568
Euler totient φ(n)	7200
Square	992250000
Cube	31255875000000
Square root	177.482393 (= 30√35)
Digit sum / digital root	9 / 9
Collatz steps to 1	129
Scientific notation	3.15 × $10^{4}$

31500 in other forms

Form	Value
In words	thirty-one thousand five hundred
Binary (base 2)	111101100001100
Octal (base 8)	75414
Hexadecimal (base 16)	7B0C
Base 3	1121012200
As time	31500 seconds = 8 h 45 min 0 s

Is 31500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (31500 ÷ 2 = 15750)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (31500 ÷ 3 = 10500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (31500 ÷ 4 = 7875)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (31500 ÷ 5 = 6300)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (31500 ÷ 6 = 5250)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (31500 ÷ 7 = 4500)	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	Yes (31500 ÷ 9 = 3500)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (31500 ÷ 10 = 3150)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 7)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (31500 ÷ 12 = 2625)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 31500 a prime number?

No. 31500 = $2^{2}$ × $3^{2}$ × $5^{3}$ × 7, so it is divisible by 2.

What are the factors of 31500?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 125, 126, 140, 150, 175, 180, 210, 225, 250, 252, 300, 315, 350, 375, 420, 450, 500, 525, 630, 700, 750, 875, 900, 1050, 1125, 1260, 1500, 1575, 1750, 2100, 2250, 2625, 3150, 3500, 4500, 5250, 6300, 7875, 10500, 15750, 31500.

What is 31500 in binary?

111101100001100 (hexadecimal 7B0C, octal 75414).

What is the square root of 31500?

About 177.4824, exactly 30√35.

Is 31500 divisible by 3?

Yes. Its digits add up to 9, a multiple of 3.

What is special about the number 31500?

31500 is a Harshad number: divisible by its digit sum 9.