The number 80100

Q: Is 80100 a prime number?

No. 80100 = 2^2 × 3^2 × 5^2 × 89, so it is divisible by 2.

80100 is a composite number with 54 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × $5^{2}$ × 89. Divisors (54): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45 … 80100.

Number

Pick any whole number from 1 to 100,000.

80100 = 2^{2} \times 3^{2} \times 5^{2} \times 89

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How to work it out

1
What is special about 80100: a Harshad number: divisible by its digit sum 9.
2
80100 is composite. Its prime factorisation is
$80100 = 2^{2} \times 3^{2} \times 5^{2} \times 89$
3
The divisors add up to 253890; without 80100 itself that is 173790, so 80100 is abundant (173790 is more than 80100). Euler's totient φ(80100) = 21120 numbers up to 80100 share no factor with it.
4
The digits of 80100 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.

LaTeX source of the formulas on this page

\[ 80100 = 2^{2} \times 3^{2} \times 5^{2} \times 89 \]

80100 at a glance

Property	Value
Type	composite
Number of divisors	54
Sum of divisors	253890
Euler totient φ(n)	21120
Square	6416010000
Cube	513922401000000
Square root	283.019434 (= 30√89)
Digit sum / digital root	9 / 9
Collatz steps to 1	138
Scientific notation	8.01 × $10^{4}$

80100 in other forms

Form	Value
In words	eighty thousand one hundred
Binary (base 2)	10011100011100100
Octal (base 8)	234344
Hexadecimal (base 16)	138E4
Base 3	11001212200
As time	80100 seconds = 22 h 15 min 0 s

Is 80100 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (80100 ÷ 2 = 40050)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (80100 ÷ 3 = 26700)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (80100 ÷ 4 = 20025)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (80100 ÷ 5 = 16020)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (80100 ÷ 6 = 13350)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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 (80100 ÷ 9 = 8900)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (80100 ÷ 10 = 8010)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 9)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (80100 ÷ 12 = 6675)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 80100 a prime number?

No. 80100 = $2^{2}$ × $3^{2}$ × $5^{2}$ × 89, so it is divisible by 2.

What are the factors of 80100?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 89, 90, 100, 150, 178, 180, 225, 267, 300, 356, 445, 450, 534, 801, 890, 900, 1068, 1335, 1602, 1780, 2225, 2670, 3204, 4005, 4450, 5340, 6675, 8010, 8900, 13350, 16020, 20025, 26700, 40050, 80100.

What is 80100 in binary?

10011100011100100 (hexadecimal 138E4, octal 234344).

What is the square root of 80100?

About 283.0194, exactly 30√89.

Is 80100 divisible by 3?

Yes. Its digits add up to 9, a multiple of 3.

What is special about the number 80100?

80100 is a Harshad number: divisible by its digit sum 9.