The number 87100

Q: Is 87100 a prime number?

No. 87100 = 2^2 × 5^2 × 13 × 67, so it is divisible by 2.

87100 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × $5^{2}$ × 13 × 67. Divisors (36): 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 67, 100, 130, 134 … 87100.

Number

Pick any whole number from 1 to 100,000.

87100 = 2^{2} \times 5^{2} \times 13 \times 67

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How to work it out

1
87100 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
87100 is composite. Its prime factorisation is
$87100 = 2^{2} \times 5^{2} \times 13 \times 67$
3
The divisors add up to 206584; without 87100 itself that is 119484, so 87100 is abundant (119484 is more than 87100). Euler's totient φ(87100) = 31680 numbers up to 87100 share no factor with it.
4
The digits of 87100 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.

LaTeX source of the formulas on this page

\[ 87100 = 2^{2} \times 5^{2} \times 13 \times 67 \]

87100 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	206584
Euler totient φ(n)	31680
Square	7586410000
Cube	660776311000000
Square root	295.127091 (= 10√871)
Digit sum / digital root	16 / 7
Collatz steps to 1	120
Scientific notation	8.71 × $10^{4}$

87100 in other forms

Form	Value
In words	eighty-seven thousand one hundred
Binary (base 2)	10101010000111100
Octal (base 8)	252074
Hexadecimal (base 16)	1543C
Base 3	11102110221
As time	87100 seconds = 24 h 11 min 40 s

Is 87100 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (87100 ÷ 2 = 43550)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 1)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (87100 ÷ 4 = 21775)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (87100 ÷ 5 = 17420)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 4)	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	No (remainder 7)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (87100 ÷ 10 = 8710)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 87100 a prime number?

No. 87100 = $2^{2}$ × $5^{2}$ × 13 × 67, so it is divisible by 2.

What are the factors of 87100?

1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 67, 100, 130, 134, 260, 268, 325, 335, 650, 670, 871, 1300, 1340, 1675, 1742, 3350, 3484, 4355, 6700, 8710, 17420, 21775, 43550, 87100.

What is 87100 in binary?

10101010000111100 (hexadecimal 1543C, octal 252074).

What is the square root of 87100?

About 295.1271, exactly 10√871.

Is 87100 divisible by 3?

No. Its digits add up to 16, which is not a multiple of 3.

What is special about the number 87100?

It is a composite number with 36 divisors.