The number 31620

Q: Is 31620 a prime number?

No. 31620 = 2^2 × 3 × 5 × 17 × 31, so it is divisible by 2.

31620 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 17 × 31. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 31, 34, 51, 60 … 31620.

Number

Pick any whole number from 1 to 100,000.

31620 = 2^{2} \times 3 \times 5 \times 17 \times 31

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

How to work it out

1
What is special about 31620: a Harshad number: divisible by its digit sum 12.
2
31620 is composite. Its prime factorisation is
$31620 = 2^{2} \times 3 \times 5 \times 17 \times 31$
3
The divisors add up to 96768; without 31620 itself that is 65148, so 31620 is abundant (65148 is more than 31620). Euler's totient φ(31620) = 7680 numbers up to 31620 share no factor with it.
4
The digits of 31620 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 191 steps to reach 1.

LaTeX source of the formulas on this page

\[ 31620 = 2^{2} \times 3 \times 5 \times 17 \times 31 \]

31620 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	96768
Euler totient φ(n)	7680
Square	999824400
Cube	31614447528000
Square root	177.820134 (= 2√7905)
Digit sum / digital root	12 / 3
Collatz steps to 1	191
Scientific notation	3.162 × $10^{4}$

31620 in other forms

Form	Value
In words	thirty-one thousand six hundred and twenty
Binary (base 2)	111101110000100
Octal (base 8)	75604
Hexadecimal (base 16)	7B84
Base 3	1121101010
As time	31620 seconds = 8 h 47 min 0 s

Is 31620 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (31620 ÷ 2 = 15810)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (31620 ÷ 3 = 10540)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (31620 ÷ 4 = 7905)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (31620 ÷ 5 = 6324)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (31620 ÷ 6 = 5270)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (31620 ÷ 10 = 3162)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (31620 ÷ 12 = 2635)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 31620 a prime number?

No. 31620 = $2^{2}$ × 3 × 5 × 17 × 31, so it is divisible by 2.

What are the factors of 31620?

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 31, 34, 51, 60, 62, 68, 85, 93, 102, 124, 155, 170, 186, 204, 255, 310, 340, 372, 465, 510, 527, 620, 930, 1020, 1054, 1581, 1860, 2108, 2635, 3162, 5270, 6324, 7905, 10540, 15810, 31620.

What is 31620 in binary?

111101110000100 (hexadecimal 7B84, octal 75604).

What is the square root of 31620?

About 177.8201, exactly 2√7905.

Is 31620 divisible by 3?

Yes. Its digits add up to 12, a multiple of 3.

What is special about the number 31620?

31620 is a Harshad number: divisible by its digit sum 12.