The number 80724

Q: Is 80724 a prime number?

No. 80724 = 2^2 × 3 × 7 × 31^2, so it is divisible by 2.

80724 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 3 × 7 × $31^{2}$ . Divisors (36): 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 31, 42, 62, 84, 93, 124 … 80724.

Number

Pick any whole number from 1 to 100,000.

80724 = 2^{2} \times 3 \times 7 \times 31^{2}

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How to work it out

1
What is special about 80724: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
2
80724 is composite. Its prime factorisation is
$80724 = 2^{2} \times 3 \times 7 \times 31^{2}$
3
The divisors add up to 222432; without 80724 itself that is 141708, so 80724 is abundant (141708 is more than 80724). Euler's totient φ(80724) = 22320 numbers up to 80724 share no factor with it.
4
The digits of 80724 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 45 steps to reach 1.

LaTeX source of the formulas on this page

\[ 80724 = 2^{2} \times 3 \times 7 \times 31^{2} \]

80724 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	222432
Euler totient φ(n)	22320
Square	6516364176
Cube	526026981743424
Square root	284.119693 (= 62√21)
Digit sum / digital root	21 / 3
Collatz steps to 1	45
Scientific notation	8.0724 × $10^{4}$

80724 in other forms

Form	Value
In words	eighty thousand seven hundred and twenty-four
Binary (base 2)	10011101101010100
Octal (base 8)	235524
Hexadecimal (base 16)	13B54
Base 3	11002201210
As time	80724 seconds = 22 h 25 min 24 s

Is 80724 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (80724 ÷ 2 = 40362)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (80724 ÷ 3 = 26908)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (80724 ÷ 4 = 20181)	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	Yes (80724 ÷ 6 = 13454)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (80724 ÷ 7 = 11532)	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 3)	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 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (80724 ÷ 12 = 6727)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 80724 a prime number?

No. 80724 = $2^{2}$ × 3 × 7 × $31^{2}$ , so it is divisible by 2.

What are the factors of 80724?

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 31, 42, 62, 84, 93, 124, 186, 217, 372, 434, 651, 868, 961, 1302, 1922, 2604, 2883, 3844, 5766, 6727, 11532, 13454, 20181, 26908, 40362, 80724.

What is 80724 in binary?

10011101101010100 (hexadecimal 13B54, octal 235524).

What is the square root of 80724?

About 284.1197, exactly 62√21.

Is 80724 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 80724?

80724 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.