The number 87120

Q: Is 87120 a prime number?

No. 87120 = 2^4 × 3^2 × 5 × 11^2, so it is divisible by 2.

87120 is a composite number with 90 divisors. Its prime factorisation is $2^{4}$ × $3^{2}$ × 5 × $11^{2}$ . Divisors (90): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22 … 87120.

Number

Pick any whole number from 1 to 100,000.

87120 = 2^{4} \times 3^{2} \times 5 \times 11^{2}

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How to work it out

1
What is special about 87120: a Harshad number: divisible by its digit sum 18.
2
87120 is composite. Its prime factorisation is
$87120 = 2^{4} \times 3^{2} \times 5 \times 11^{2}$
3
The divisors add up to 321594; without 87120 itself that is 234474, so 87120 is abundant (234474 is more than 87120). Euler's totient φ(87120) = 21120 numbers up to 87120 share no factor with it.
4
The digits of 87120 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 58 steps to reach 1.

LaTeX source of the formulas on this page

\[ 87120 = 2^{4} \times 3^{2} \times 5 \times 11^{2} \]

87120 at a glance

Property	Value
Type	composite
Number of divisors	90
Sum of divisors	321594
Euler totient φ(n)	21120
Square	7589894400
Cube	661231600128000
Square root	295.160973 (= 132√5)
Digit sum / digital root	18 / 9
Collatz steps to 1	58
Scientific notation	8.712 × $10^{4}$

87120 in other forms

Form	Value
In words	eighty-seven thousand one hundred and twenty
Binary (base 2)	10101010001010000
Octal (base 8)	252120
Hexadecimal (base 16)	15450
Base 3	11102111200
As time	87120 seconds = 24 h 12 min 0 s

Is 87120 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (87120 ÷ 2 = 43560)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (87120 ÷ 3 = 29040)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (87120 ÷ 4 = 21780)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (87120 ÷ 5 = 17424)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (87120 ÷ 6 = 14520)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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 (87120 ÷ 8 = 10890)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (87120 ÷ 9 = 9680)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (87120 ÷ 10 = 8712)	A number is divisible by 10 if the last digit is 0.
11	Yes (87120 ÷ 11 = 7920)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (87120 ÷ 12 = 7260)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 87120 a prime number?

No. 87120 = $2^{4}$ × $3^{2}$ × 5 × $11^{2}$ , so it is divisible by 2.

What are the factors of 87120?

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 121, 132, 144, 165, 176, 180, 198, 220, 240, 242, 264, 330, 360, 363, 396, 440, 484, 495, 528, 605, 660, 720, 726, 792, 880, 968, 990, 1089, 1210, 1320, 1452, 1584, 1815, 1936, 1980, 2178, 2420, 2640, 2904, 3630, 3960, 4356, 4840, 5445, 5808, 7260, 7920, 8712, 9680, 10890, 14520, 17424, 21780, 29040, 43560, 87120.

What is 87120 in binary?

10101010001010000 (hexadecimal 15450, octal 252120).

What is the square root of 87120?

About 295.1610, exactly 132√5.

Is 87120 divisible by 3?

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

What is special about the number 87120?

87120 is a Harshad number: divisible by its digit sum 18.