The number 64000

Q: Is 64000 a prime number?

No. 64000 = 2^9 × 5^3, so it is divisible by 2.

Q: What is special about the number 64000?

64000 is a perfect cube (40^3); a Harshad number: divisible by its digit sum 10.

64000 is a perfect cube ( $40^{3}$ ). Its prime factorisation is $2^{9}$ × $5^{3}$ . Divisors (40): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125 … 64000.

Number

Pick any whole number from 1 to 100,000.

64000 = 2^{9} \times 5^{3}

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

How to work it out

1
What is special about 64000: a perfect cube ( $40^{3}$ ); a Harshad number: divisible by its digit sum 10.
2
64000 is composite. Its prime factorisation is
$64000 = 2^{9} \times 5^{3}$
3
The divisors add up to 159588; without 64000 itself that is 95588, so 64000 is abundant (95588 is more than 64000). Euler's totient φ(64000) = 25600 numbers up to 64000 share no factor with it.
4
The digits of 64000 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 117 steps to reach 1.

LaTeX source of the formulas on this page

\[ 64000 = 2^{9} \times 5^{3} \]

64000 at a glance

Property	Value
Type	composite
Number of divisors	40
Sum of divisors	159588
Euler totient φ(n)	25600
Square	4096000000
Cube	262144000000000
Square root	252.982213 (= 80√10)
Digit sum / digital root	10 / 1
Collatz steps to 1	117
Scientific notation	6.4 × $10^{4}$
Perfect power	$40^{3}$

64000 in other forms

Form	Value
In words	sixty-four thousand
Binary (base 2)	1111101000000000
Octal (base 8)	175000
Hexadecimal (base 16)	FA00
Base 3	10020210101
As time	64000 seconds = 17 h 46 min 40 s

Is 64000 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (64000 ÷ 2 = 32000)	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 (64000 ÷ 4 = 16000)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (64000 ÷ 5 = 12800)	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 6)	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 (64000 ÷ 8 = 8000)	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	Yes (64000 ÷ 10 = 6400)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	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 64000 a prime number?

No. 64000 = $2^{9}$ × $5^{3}$ , so it is divisible by 2.

What are the factors of 64000?

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 640, 800, 1000, 1280, 1600, 2000, 2560, 3200, 4000, 6400, 8000, 12800, 16000, 32000, 64000.

What is 64000 in binary?

1111101000000000 (hexadecimal FA00, octal 175000).

What is the square root of 64000?

About 252.9822, exactly 80√10.

Is 64000 divisible by 3?

No. Its digits add up to 10, which is not a multiple of 3.

What is special about the number 64000?

64000 is a perfect cube ( $40^{3}$ ); a Harshad number: divisible by its digit sum 10.