The number 72600

Q: Is 72600 a prime number?

No. 72600 = 2^3 × 3 × 5^2 × 11^2, so it is divisible by 2.

72600 is a composite number with 72 divisors. Its prime factorisation is $2^{3}$ × 3 × $5^{2}$ × $11^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30 … 72600.

Number

Pick any whole number from 1 to 100,000.

72600 = 2^{3} \times 3 \times 5^{2} \times 11^{2}

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

How to work it out

1
What is special about 72600: a Harshad number: divisible by its digit sum 15.
2
72600 is composite. Its prime factorisation is
$72600 = 2^{3} \times 3 \times 5^{2} \times 11^{2}$
3
The divisors add up to 247380; without 72600 itself that is 174780, so 72600 is abundant (174780 is more than 72600). Euler's totient φ(72600) = 17600 numbers up to 72600 share no factor with it.
4
The digits of 72600 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.

LaTeX source of the formulas on this page

\[ 72600 = 2^{3} \times 3 \times 5^{2} \times 11^{2} \]

72600 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	247380
Euler totient φ(n)	17600
Square	5270760000
Cube	382657176000000
Square root	269.443872 (= 110√6)
Digit sum / digital root	15 / 6
Collatz steps to 1	68
Scientific notation	7.26 × $10^{4}$

72600 in other forms

Form	Value
In words	seventy-two thousand six hundred
Binary (base 2)	10001101110011000
Octal (base 8)	215630
Hexadecimal (base 16)	11B98
Base 3	10200120220
As time	72600 seconds = 20 h 10 min 0 s

Is 72600 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (72600 ÷ 2 = 36300)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (72600 ÷ 3 = 24200)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (72600 ÷ 4 = 18150)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (72600 ÷ 5 = 14520)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (72600 ÷ 6 = 12100)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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 (72600 ÷ 8 = 9075)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (72600 ÷ 10 = 7260)	A number is divisible by 10 if the last digit is 0.
11	Yes (72600 ÷ 11 = 6600)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (72600 ÷ 12 = 6050)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 72600 a prime number?

No. 72600 = $2^{3}$ × 3 × $5^{2}$ × $11^{2}$ , so it is divisible by 2.

What are the factors of 72600?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 40, 44, 50, 55, 60, 66, 75, 88, 100, 110, 120, 121, 132, 150, 165, 200, 220, 242, 264, 275, 300, 330, 363, 440, 484, 550, 600, 605, 660, 726, 825, 968, 1100, 1210, 1320, 1452, 1650, 1815, 2200, 2420, 2904, 3025, 3300, 3630, 4840, 6050, 6600, 7260, 9075, 12100, 14520, 18150, 24200, 36300, 72600.

What is 72600 in binary?

10001101110011000 (hexadecimal 11B98, octal 215630).

What is the square root of 72600?

About 269.4439, exactly 110√6.

Is 72600 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 72600?

72600 is a Harshad number: divisible by its digit sum 15.