The number 67600

Q: Is 67600 a prime number?

No. 67600 = 2^4 × 5^2 × 13^2, so it is divisible by 2.

67600 is a perfect square (260²). Its prime factorisation is $2^{4}$ × $5^{2}$ × $13^{2}$ . Divisors (45): 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80 … 67600.

Number

Pick any whole number from 1 to 100,000.

67600 = 2^{4} \times 5^{2} \times 13^{2}

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How to work it out

1
What is special about 67600: a perfect square (260²).
2
67600 is composite. Its prime factorisation is
$67600 = 2^{4} \times 5^{2} \times 13^{2}$
3
The divisors add up to 175863; without 67600 itself that is 108263, so 67600 is abundant (108263 is more than 67600). Euler's totient φ(67600) = 24960 numbers up to 67600 share no factor with it.
4
The digits of 67600 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 60 steps to reach 1.

LaTeX source of the formulas on this page

\[ 67600 = 2^{4} \times 5^{2} \times 13^{2} \]

67600 at a glance

Property	Value
Type	composite
Number of divisors	45
Sum of divisors	175863
Euler totient φ(n)	24960
Square	4569760000
Cube	308915776000000
Square root	260
Digit sum / digital root	19 / 1
Collatz steps to 1	60
Scientific notation	6.76 × $10^{4}$
Perfect power	$260^{2}$

67600 in other forms

Form	Value
In words	sixty-seven thousand six hundred
Binary (base 2)	10000100000010000
Octal (base 8)	204020
Hexadecimal (base 16)	10810
Base 3	10102201201
As time	67600 seconds = 18 h 46 min 40 s

Is 67600 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (67600 ÷ 2 = 33800)	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 (67600 ÷ 4 = 16900)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (67600 ÷ 5 = 13520)	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 (67600 ÷ 8 = 8450)	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 (67600 ÷ 10 = 6760)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	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 67600 a prime number?

No. 67600 = $2^{4}$ × $5^{2}$ × $13^{2}$ , so it is divisible by 2.

What are the factors of 67600?

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 169, 200, 208, 260, 325, 338, 400, 520, 650, 676, 845, 1040, 1300, 1352, 1690, 2600, 2704, 3380, 4225, 5200, 6760, 8450, 13520, 16900, 33800, 67600.

What is 67600 in binary?

10000100000010000 (hexadecimal 10810, octal 204020).

What is the square root of 67600?

260, because 260 × 260 = 67600.

Is 67600 divisible by 3?

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

What is special about the number 67600?

67600 is a perfect square (260²).