The number 75348

Q: Is 75348 a prime number?

No. 75348 = 2^2 × 3^2 × 7 × 13 × 23, so it is divisible by 2.

75348 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 7 × 13 × 23. Divisors (72): 1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 23, 26, 28, 36 … 75348.

Number

Pick any whole number from 1 to 100,000.

75348 = 2^{2} \times 3^{2} \times 7 \times 13 \times 23

Explain it step by step in chat Make a short video of it

How to work it out

1
75348 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
75348 is composite. Its prime factorisation is
$75348 = 2^{2} \times 3^{2} \times 7 \times 13 \times 23$
3
The divisors add up to 244608; without 75348 itself that is 169260, so 75348 is abundant (169260 is more than 75348). Euler's totient φ(75348) = 19008 numbers up to 75348 share no factor with it.
4
The digits of 75348 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.

LaTeX source of the formulas on this page

\[ 75348 = 2^{2} \times 3^{2} \times 7 \times 13 \times 23 \]

75348 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	244608
Euler totient φ(n)	19008
Square	5677321104
Cube	427774790544192
Square root	274.495902 (= 6√2093)
Digit sum / digital root	27 / 9
Collatz steps to 1	37
Scientific notation	7.5348 × $10^{4}$

75348 in other forms

Form	Value
In words	seventy-five thousand three hundred and forty-eight
Binary (base 2)	10010011001010100
Octal (base 8)	223124
Hexadecimal (base 16)	12654
Base 3	10211100200
As time	75348 seconds = 20 h 55 min 48 s

Is 75348 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (75348 ÷ 2 = 37674)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (75348 ÷ 3 = 25116)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (75348 ÷ 4 = 18837)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (75348 ÷ 6 = 12558)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (75348 ÷ 7 = 10764)	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 (75348 ÷ 9 = 8372)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 8)	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 (75348 ÷ 12 = 6279)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 75348 a prime number?

No. 75348 = $2^{2}$ × $3^{2}$ × 7 × 13 × 23, so it is divisible by 2.

What are the factors of 75348?

1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 23, 26, 28, 36, 39, 42, 46, 52, 63, 69, 78, 84, 91, 92, 117, 126, 138, 156, 161, 182, 207, 234, 252, 273, 276, 299, 322, 364, 414, 468, 483, 546, 598, 644, 819, 828, 897, 966, 1092, 1196, 1449, 1638, 1794, 1932, 2093, 2691, 2898, 3276, 3588, 4186, 5382, 5796, 6279, 8372, 10764, 12558, 18837, 25116, 37674, 75348.

What is 75348 in binary?

10010011001010100 (hexadecimal 12654, octal 223124).

What is the square root of 75348?

About 274.4959, exactly 6√2093.

Is 75348 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 75348?

It is a composite number with 72 divisors.