The number 21952

Q: Is 21952 a prime number?

No. 21952 = 2^6 × 7^3, so it is divisible by 2.

Q: What is special about the number 21952?

21952 is a perfect cube (28^3).

21952 is a perfect cube ( $28^{3}$ ). Its prime factorisation is $2^{6}$ × $7^{3}$ . Divisors (28): 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224 … 21952.

Number

Pick any whole number from 1 to 100,000.

21952 = 2^{6} \times 7^{3}

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How to work it out

1
What is special about 21952: a perfect cube ( $28^{3}$ ).
2
21952 is composite. Its prime factorisation is
$21952 = 2^{6} \times 7^{3}$
3
The divisors add up to 50800; without 21952 itself that is 28848, so 21952 is abundant (28848 is more than 21952). Euler's totient φ(21952) = 9408 numbers up to 21952 share no factor with it.
4
The digits of 21952 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 131 steps to reach 1.

LaTeX source of the formulas on this page

\[ 21952 = 2^{6} \times 7^{3} \]

21952 at a glance

Property	Value
Type	composite
Number of divisors	28
Sum of divisors	50800
Euler totient φ(n)	9408
Square	481890304
Cube	10578455953408
Square root	148.162073 (= 56√7)
Digit sum / digital root	19 / 1
Collatz steps to 1	131
Scientific notation	2.1952 × $10^{4}$
Perfect power	$28^{3}$

21952 in other forms

Form	Value
In words	twenty-one thousand nine hundred and fifty-two
Binary (base 2)	101010111000000
Octal (base 8)	52700
Hexadecimal (base 16)	55C0
Base 3	1010010001
As time	21952 seconds = 6 h 5 min 52 s

Is 21952 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (21952 ÷ 2 = 10976)	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 (21952 ÷ 4 = 5488)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 2)	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	Yes (21952 ÷ 7 = 3136)	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	Yes (21952 ÷ 8 = 2744)	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	No (remainder 2)	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	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 21952 a prime number?

No. 21952 = $2^{6}$ × $7^{3}$ , so it is divisible by 2.

What are the factors of 21952?

1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 343, 392, 448, 686, 784, 1372, 1568, 2744, 3136, 5488, 10976, 21952.

What is 21952 in binary?

101010111000000 (hexadecimal 55C0, octal 52700).

What is the square root of 21952?

About 148.1621, exactly 56√7.

Is 21952 divisible by 3?

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

What is special about the number 21952?

21952 is a perfect cube ( $28^{3}$ ).