The number 26460

Q: Is 26460 a prime number?

No. 26460 = 2^2 × 3^3 × 5 × 7^2, so it is divisible by 2.

26460 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × 5 × $7^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27 … 26460.

Number

Pick any whole number from 1 to 100,000.

26460 = 2^{2} \times 3^{3} \times 5 \times 7^{2}

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

How to work it out

1
What is special about 26460: a Harshad number: divisible by its digit sum 18.
2
26460 is composite. Its prime factorisation is
$26460 = 2^{2} \times 3^{3} \times 5 \times 7^{2}$
3
The divisors add up to 95760; without 26460 itself that is 69300, so 26460 is abundant (69300 is more than 26460). Euler's totient φ(26460) = 6048 numbers up to 26460 share no factor with it.
4
The digits of 26460 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 77 steps to reach 1.

LaTeX source of the formulas on this page

\[ 26460 = 2^{2} \times 3^{3} \times 5 \times 7^{2} \]

26460 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	95760
Euler totient φ(n)	6048
Square	700131600
Cube	18525482136000
Square root	162.665301 (= 42√15)
Digit sum / digital root	18 / 9
Collatz steps to 1	77
Scientific notation	2.646 × $10^{4}$

26460 in other forms

Form	Value
In words	twenty-six thousand four hundred and sixty
Binary (base 2)	110011101011100
Octal (base 8)	63534
Hexadecimal (base 16)	675C
Base 3	1100022000
As time	26460 seconds = 7 h 21 min 0 s

Is 26460 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (26460 ÷ 2 = 13230)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (26460 ÷ 3 = 8820)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (26460 ÷ 4 = 6615)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (26460 ÷ 5 = 5292)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (26460 ÷ 6 = 4410)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (26460 ÷ 7 = 3780)	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	Yes (26460 ÷ 9 = 2940)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (26460 ÷ 10 = 2646)	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	Yes (26460 ÷ 12 = 2205)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 26460 a prime number?

No. 26460 = $2^{2}$ × $3^{3}$ × 5 × $7^{2}$ , so it is divisible by 2.

What are the factors of 26460?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 49, 54, 60, 63, 70, 84, 90, 98, 105, 108, 126, 135, 140, 147, 180, 189, 196, 210, 245, 252, 270, 294, 315, 378, 420, 441, 490, 540, 588, 630, 735, 756, 882, 945, 980, 1260, 1323, 1470, 1764, 1890, 2205, 2646, 2940, 3780, 4410, 5292, 6615, 8820, 13230, 26460.

What is 26460 in binary?

110011101011100 (hexadecimal 675C, octal 63534).

What is the square root of 26460?

About 162.6653, exactly 42√15.

Is 26460 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 26460?

26460 is a Harshad number: divisible by its digit sum 18.