The number 73788

Q: Is 73788 a prime number?

No. 73788 = 2^2 × 3 × 11 × 13 × 43, so it is divisible by 2.

73788 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 11 × 13 × 43. Divisors (48): 1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 39, 43, 44, 52, 66 … 73788.

Number

Pick any whole number from 1 to 100,000.

73788 = 2^{2} \times 3 \times 11 \times 13 \times 43

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

How to work it out

1
What is special about 73788: a Harshad number: divisible by its digit sum 33.
2
73788 is composite. Its prime factorisation is
$73788 = 2^{2} \times 3 \times 11 \times 13 \times 43$
3
The divisors add up to 206976; without 73788 itself that is 133188, so 73788 is abundant (133188 is more than 73788). Euler's totient φ(73788) = 20160 numbers up to 73788 share no factor with it.
4
The digits of 73788 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.

LaTeX source of the formulas on this page

\[ 73788 = 2^{2} \times 3 \times 11 \times 13 \times 43 \]

73788 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	206976
Euler totient φ(n)	20160
Square	5444668944
Cube	401751232039872
Square root	271.639467 (= 2√18447)
Digit sum / digital root	33 / 6
Collatz steps to 1	50
Scientific notation	7.3788 × $10^{4}$

73788 in other forms

Form	Value
In words	seventy-three thousand seven hundred and eighty-eight
Binary (base 2)	10010000000111100
Octal (base 8)	220074
Hexadecimal (base 16)	1203C
Base 3	10202012220
As time	73788 seconds = 20 h 29 min 48 s

Is 73788 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (73788 ÷ 2 = 36894)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (73788 ÷ 3 = 24596)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (73788 ÷ 4 = 18447)	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 (73788 ÷ 6 = 12298)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 6)	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	Yes (73788 ÷ 11 = 6708)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (73788 ÷ 12 = 6149)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 73788 a prime number?

No. 73788 = $2^{2}$ × 3 × 11 × 13 × 43, so it is divisible by 2.

What are the factors of 73788?

1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 39, 43, 44, 52, 66, 78, 86, 129, 132, 143, 156, 172, 258, 286, 429, 473, 516, 559, 572, 858, 946, 1118, 1419, 1677, 1716, 1892, 2236, 2838, 3354, 5676, 6149, 6708, 12298, 18447, 24596, 36894, 73788.

What is 73788 in binary?

10010000000111100 (hexadecimal 1203C, octal 220074).

What is the square root of 73788?

About 271.6395, exactly 2√18447.

Is 73788 divisible by 3?

Yes. Its digits add up to 33, a multiple of 3.

What is special about the number 73788?

73788 is a Harshad number: divisible by its digit sum 33.