The number 64

No. 64 = 2^6, so it is divisible by 2.

64 is a power of 2 (2^6); a perfect square (8²).

64 is a power of 2 ( $2^{6}$ ) and a perfect square (8²). Its prime factorisation is $2^{6}$ . Divisors (7): 1, 2, 4, 8, 16, 32, 64.

Number

Pick any whole number from 1 to 100,000.

64 = 2^{6}

How to work it out

1
What is special about 64: a power of 2 ( $2^{6}$ ); a perfect square (8²).
2
64 is composite. Its prime factorisation is
$64 = 2^{6}$
3
The divisors add up to 127; without 64 itself that is 63, so 64 is deficient (63 is less than 64). Euler's totient φ(64) = 32 numbers up to 64 share no factor with it.
4
The digits of 64 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 6 steps to reach 1.

LaTeX source of the formulas on this page

\[ 64 = 2^{6} \]

Divisor	Answer	Rule
2	Yes (64 ÷ 2 = 32)	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 (64 ÷ 4 = 16)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	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 (64 ÷ 8 = 8)	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 4)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	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.

Is 64 a prime number?

No. 64 = $2^{6}$ , so it is divisible by 2.

What are the factors of 64?

1, 2, 4, 8, 16, 32, 64.

What is 64 in binary?

1000000 (hexadecimal 40, octal 100).

What is the square root of 64?

8, because 8 × 8 = 64.

What is 64 in Roman numerals?

LXIV.

Is 64 divisible by 3?

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

What is special about the number 64?

64 is a power of 2 ( $2^{6}$ ); a perfect square (8²).