The number 31460

Q: Is 31460 a prime number?

No. 31460 = 2^2 × 5 × 11^2 × 13, so it is divisible by 2.

31460 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 5 × $11^{2}$ × 13. Divisors (36): 1, 2, 4, 5, 10, 11, 13, 20, 22, 26, 44, 52, 55, 65, 110, 121 … 31460.

Number

Pick any whole number from 1 to 100,000.

31460 = 2^{2} \times 5 \times 11^{2} \times 13

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

How to work it out

1
31460 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
31460 is composite. Its prime factorisation is
$31460 = 2^{2} \times 5 \times 11^{2} \times 13$
3
The divisors add up to 78204; without 31460 itself that is 46744, so 31460 is abundant (46744 is more than 31460). Euler's totient φ(31460) = 10560 numbers up to 31460 share no factor with it.
4
The digits of 31460 add up to 14, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.

LaTeX source of the formulas on this page

\[ 31460 = 2^{2} \times 5 \times 11^{2} \times 13 \]

31460 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	78204
Euler totient φ(n)	10560
Square	989731600
Cube	31136956136000
Square root	177.369670 (= 22√65)
Digit sum / digital root	14 / 5
Collatz steps to 1	54
Scientific notation	3.146 × $10^{4}$

31460 in other forms

Form	Value
In words	thirty-one thousand four hundred and sixty
Binary (base 2)	111101011100100
Octal (base 8)	75344
Hexadecimal (base 16)	7AE4
Base 3	1121011012
As time	31460 seconds = 8 h 44 min 20 s

Is 31460 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (31460 ÷ 2 = 15730)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (31460 ÷ 4 = 7865)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (31460 ÷ 5 = 6292)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 2)	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 5)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (31460 ÷ 10 = 3146)	A number is divisible by 10 if the last digit is 0.
11	Yes (31460 ÷ 11 = 2860)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 31460 a prime number?

No. 31460 = $2^{2}$ × 5 × $11^{2}$ × 13, so it is divisible by 2.

What are the factors of 31460?

1, 2, 4, 5, 10, 11, 13, 20, 22, 26, 44, 52, 55, 65, 110, 121, 130, 143, 220, 242, 260, 286, 484, 572, 605, 715, 1210, 1430, 1573, 2420, 2860, 3146, 6292, 7865, 15730, 31460.

What is 31460 in binary?

111101011100100 (hexadecimal 7AE4, octal 75344).

What is the square root of 31460?

About 177.3697, exactly 22√65.

Is 31460 divisible by 3?

No. Its digits add up to 14, which is not a multiple of 3.

What is special about the number 31460?

It is a composite number with 36 divisors.