The number 26180

Q: Is 26180 a prime number?

No. 26180 = 2^2 × 5 × 7 × 11 × 17, so it is divisible by 2.

26180 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 5 × 7 × 11 × 17. Divisors (48): 1, 2, 4, 5, 7, 10, 11, 14, 17, 20, 22, 28, 34, 35, 44, 55 … 26180.

Number

Pick any whole number from 1 to 100,000.

26180 = 2^{2} \times 5 \times 7 \times 11 \times 17

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

How to work it out

1
What is special about 26180: a Harshad number: divisible by its digit sum 17.
2
26180 is composite. Its prime factorisation is
$26180 = 2^{2} \times 5 \times 7 \times 11 \times 17$
3
The divisors add up to 72576; without 26180 itself that is 46396, so 26180 is abundant (46396 is more than 26180). Euler's totient φ(26180) = 7680 numbers up to 26180 share no factor with it.
4
The digits of 26180 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 139 steps to reach 1.

LaTeX source of the formulas on this page

\[ 26180 = 2^{2} \times 5 \times 7 \times 11 \times 17 \]

26180 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	72576
Euler totient φ(n)	7680
Square	685392400
Cube	17943573032000
Square root	161.802349 (= 2√6545)
Digit sum / digital root	17 / 8
Collatz steps to 1	139
Scientific notation	2.618 × $10^{4}$

26180 in other forms

Form	Value
In words	twenty-six thousand one hundred and eighty
Binary (base 2)	110011001000100
Octal (base 8)	63104
Hexadecimal (base 16)	6644
Base 3	1022220122
As time	26180 seconds = 7 h 16 min 20 s

Is 26180 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (26180 ÷ 2 = 13090)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (26180 ÷ 4 = 6545)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (26180 ÷ 5 = 5236)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 2)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (26180 ÷ 7 = 3740)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 8)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (26180 ÷ 10 = 2618)	A number is divisible by 10 if the last digit is 0.
11	Yes (26180 ÷ 11 = 2380)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 26180 a prime number?

No. 26180 = $2^{2}$ × 5 × 7 × 11 × 17, so it is divisible by 2.

What are the factors of 26180?

1, 2, 4, 5, 7, 10, 11, 14, 17, 20, 22, 28, 34, 35, 44, 55, 68, 70, 77, 85, 110, 119, 140, 154, 170, 187, 220, 238, 308, 340, 374, 385, 476, 595, 748, 770, 935, 1190, 1309, 1540, 1870, 2380, 2618, 3740, 5236, 6545, 13090, 26180.

What is 26180 in binary?

110011001000100 (hexadecimal 6644, octal 63104).

What is the square root of 26180?

About 161.8023, exactly 2√6545.

Is 26180 divisible by 3?

No. Its digits add up to 17, which is not a multiple of 3.

What is special about the number 26180?

26180 is a Harshad number: divisible by its digit sum 17.