The number 78120

Q: Is 78120 a prime number?

No. 78120 = 2^3 × 3^2 × 5 × 7 × 31, so it is divisible by 2.

78120 is a composite number with 96 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × 5 × 7 × 31. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21 … 78120.

Number

Pick any whole number from 1 to 100,000.

78120 = 2^{3} \times 3^{2} \times 5 \times 7 \times 31

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How to work it out

1
What is special about 78120: a Harshad number: divisible by its digit sum 18.
2
78120 is composite. Its prime factorisation is
$78120 = 2^{3} \times 3^{2} \times 5 \times 7 \times 31$
3
The divisors add up to 299520; without 78120 itself that is 221400, so 78120 is abundant (221400 is more than 78120). Euler's totient φ(78120) = 17280 numbers up to 78120 share no factor with it.
4
The digits of 78120 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 76 steps to reach 1.

LaTeX source of the formulas on this page

\[ 78120 = 2^{3} \times 3^{2} \times 5 \times 7 \times 31 \]

78120 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	299520
Euler totient φ(n)	17280
Square	6102734400
Cube	476745611328000
Square root	279.499553 (= 6√2170)
Digit sum / digital root	18 / 9
Collatz steps to 1	76
Scientific notation	7.812 × $10^{4}$

78120 in other forms

Form	Value
In words	seventy-eight thousand one hundred and twenty
Binary (base 2)	10011000100101000
Octal (base 8)	230450
Hexadecimal (base 16)	13128
Base 3	10222011100
As time	78120 seconds = 21 h 42 min 0 s

Is 78120 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (78120 ÷ 2 = 39060)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (78120 ÷ 3 = 26040)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (78120 ÷ 4 = 19530)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (78120 ÷ 5 = 15624)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (78120 ÷ 6 = 13020)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (78120 ÷ 7 = 11160)	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 (78120 ÷ 8 = 9765)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (78120 ÷ 9 = 8680)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (78120 ÷ 10 = 7812)	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 (78120 ÷ 12 = 6510)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 78120 a prime number?

No. 78120 = $2^{3}$ × $3^{2}$ × 5 × 7 × 31, so it is divisible by 2.

What are the factors of 78120?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 31, 35, 36, 40, 42, 45, 56, 60, 62, 63, 70, 72, 84, 90, 93, 105, 120, 124, 126, 140, 155, 168, 180, 186, 210, 217, 248, 252, 279, 280, 310, 315, 360, 372, 420, 434, 465, 504, 558, 620, 630, 651, 744, 840, 868, 930, 1085, 1116, 1240, 1260, 1302, 1395, 1736, 1860, 1953, 2170, 2232, 2520, 2604, 2790, 3255, 3720, 3906, 4340, 5208, 5580, 6510, 7812, 8680, 9765, 11160, 13020, 15624, 19530, 26040, 39060, 78120.

What is 78120 in binary?

10011000100101000 (hexadecimal 13128, octal 230450).

What is the square root of 78120?

About 279.4996, exactly 6√2170.

Is 78120 divisible by 3?

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

What is special about the number 78120?

78120 is a Harshad number: divisible by its digit sum 18.