The number 10648

Q: Is 10648 a prime number?

No. 10648 = 2^3 × 11^3, so it is divisible by 2.

Q: What is special about the number 10648?

10648 is a perfect cube (22^3).

10648 is a perfect cube ( $22^{3}$ ). Its prime factorisation is $2^{3}$ × $11^{3}$ . Divisors (16): 1, 2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 968, 1331, 2662, 5324, 10648.

Number

Pick any whole number from 1 to 100,000.

10648 = 2^{3} \times 11^{3}

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How to work it out

1
What is special about 10648: a perfect cube ( $22^{3}$ ).
2
10648 is composite. Its prime factorisation is
$10648 = 2^{3} \times 11^{3}$
3
The divisors add up to 21960; without 10648 itself that is 11312, so 10648 is abundant (11312 is more than 10648). Euler's totient φ(10648) = 4840 numbers up to 10648 share no factor with it.
4
The digits of 10648 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 55 steps to reach 1.

LaTeX source of the formulas on this page

\[ 10648 = 2^{3} \times 11^{3} \]

10648 at a glance

Property	Value
Type	composite
Number of divisors	16
Sum of divisors	21960
Euler totient φ(n)	4840
Square	113379904
Cube	1207269217792
Square root	103.189147 (= 22√22)
Digit sum / digital root	19 / 1
Collatz steps to 1	55
Scientific notation	1.0648 × $10^{4}$
Perfect power	$22^{3}$

10648 in other forms

Form	Value
In words	ten thousand six hundred and forty-eight
Binary (base 2)	10100110011000
Octal (base 8)	24630
Hexadecimal (base 16)	2998
Base 3	112121101
As time	10648 seconds = 2 h 57 min 28 s

Is 10648 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (10648 ÷ 2 = 5324)	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 (10648 ÷ 4 = 2662)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	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	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	Yes (10648 ÷ 8 = 1331)	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 8)	A number is divisible by 10 if the last digit is 0.
11	Yes (10648 ÷ 11 = 968)	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 10648 a prime number?

No. 10648 = $2^{3}$ × $11^{3}$ , so it is divisible by 2.

What are the factors of 10648?

1, 2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 968, 1331, 2662, 5324, 10648.

What is 10648 in binary?

10100110011000 (hexadecimal 2998, octal 24630).

What is the square root of 10648?

About 103.1891, exactly 22√22.

Is 10648 divisible by 3?

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

What is special about the number 10648?

10648 is a perfect cube ( $22^{3}$ ).