The number 75480

Q: Is 75480 a prime number?

No. 75480 = 2^3 × 3 × 5 × 17 × 37, so it is divisible by 2.

75480 is a composite number with 64 divisors. Its prime factorisation is $2^{3}$ × 3 × 5 × 17 × 37. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 37 … 75480.

Number

Pick any whole number from 1 to 100,000.

75480 = 2^{3} \times 3 \times 5 \times 17 \times 37

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How to work it out

1
What is special about 75480: a Harshad number: divisible by its digit sum 24.
2
75480 is composite. Its prime factorisation is
$75480 = 2^{3} \times 3 \times 5 \times 17 \times 37$
3
The divisors add up to 246240; without 75480 itself that is 170760, so 75480 is abundant (170760 is more than 75480). Euler's totient φ(75480) = 18432 numbers up to 75480 share no factor with it.
4
The digits of 75480 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 156 steps to reach 1.

LaTeX source of the formulas on this page

\[ 75480 = 2^{3} \times 3 \times 5 \times 17 \times 37 \]

75480 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	246240
Euler totient φ(n)	18432
Square	5697230400
Cube	430026950592000
Square root	274.736237 (= 2√18870)
Digit sum / digital root	24 / 6
Collatz steps to 1	156
Scientific notation	7.548 × $10^{4}$

75480 in other forms

Form	Value
In words	seventy-five thousand four hundred and eighty
Binary (base 2)	10010011011011000
Octal (base 8)	223330
Hexadecimal (base 16)	126D8
Base 3	10211112120
As time	75480 seconds = 20 h 58 min 0 s

Is 75480 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (75480 ÷ 2 = 37740)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (75480 ÷ 3 = 25160)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (75480 ÷ 4 = 18870)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (75480 ÷ 5 = 15096)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (75480 ÷ 6 = 12580)	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	Yes (75480 ÷ 8 = 9435)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (75480 ÷ 10 = 7548)	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 (75480 ÷ 12 = 6290)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 75480 a prime number?

No. 75480 = $2^{3}$ × 3 × 5 × 17 × 37, so it is divisible by 2.

What are the factors of 75480?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 37, 40, 51, 60, 68, 74, 85, 102, 111, 120, 136, 148, 170, 185, 204, 222, 255, 296, 340, 370, 408, 444, 510, 555, 629, 680, 740, 888, 1020, 1110, 1258, 1480, 1887, 2040, 2220, 2516, 3145, 3774, 4440, 5032, 6290, 7548, 9435, 12580, 15096, 18870, 25160, 37740, 75480.

What is 75480 in binary?

10010011011011000 (hexadecimal 126D8, octal 223330).

What is the square root of 75480?

About 274.7362, exactly 2√18870.

Is 75480 divisible by 3?

Yes. Its digits add up to 24, a multiple of 3.

What is special about the number 75480?

75480 is a Harshad number: divisible by its digit sum 24.