The number 38700

Q: Is 38700 a prime number?

No. 38700 = 2^2 × 3^2 × 5^2 × 43, so it is divisible by 2.

38700 is a composite number with 54 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × $5^{2}$ × 43. Divisors (54): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 43 … 38700.

Number

Pick any whole number from 1 to 100,000.

38700 = 2^{2} \times 3^{2} \times 5^{2} \times 43

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How to work it out

1
What is special about 38700: a Harshad number: divisible by its digit sum 18.
2
38700 is composite. Its prime factorisation is
$38700 = 2^{2} \times 3^{2} \times 5^{2} \times 43$
3
The divisors add up to 124124; without 38700 itself that is 85424, so 38700 is abundant (85424 is more than 38700). Euler's totient φ(38700) = 10080 numbers up to 38700 share no factor with it.
4
The digits of 38700 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 75 steps to reach 1.

LaTeX source of the formulas on this page

\[ 38700 = 2^{2} \times 3^{2} \times 5^{2} \times 43 \]

38700 at a glance

Property	Value
Type	composite
Number of divisors	54
Sum of divisors	124124
Euler totient φ(n)	10080
Square	1497690000
Cube	57960603000000
Square root	196.723156 (= 30√43)
Digit sum / digital root	18 / 9
Collatz steps to 1	75
Scientific notation	3.87 × $10^{4}$

38700 in other forms

Form	Value
In words	thirty-eight thousand seven hundred
Binary (base 2)	1001011100101100
Octal (base 8)	113454
Hexadecimal (base 16)	972C
Base 3	1222002100
As time	38700 seconds = 10 h 45 min 0 s

Is 38700 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (38700 ÷ 2 = 19350)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (38700 ÷ 3 = 12900)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (38700 ÷ 4 = 9675)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (38700 ÷ 5 = 7740)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (38700 ÷ 6 = 6450)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 4)	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 (38700 ÷ 9 = 4300)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (38700 ÷ 10 = 3870)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (38700 ÷ 12 = 3225)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 38700 a prime number?

No. 38700 = $2^{2}$ × $3^{2}$ × $5^{2}$ × 43, so it is divisible by 2.

What are the factors of 38700?

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 43, 45, 50, 60, 75, 86, 90, 100, 129, 150, 172, 180, 215, 225, 258, 300, 387, 430, 450, 516, 645, 774, 860, 900, 1075, 1290, 1548, 1935, 2150, 2580, 3225, 3870, 4300, 6450, 7740, 9675, 12900, 19350, 38700.

What is 38700 in binary?

1001011100101100 (hexadecimal 972C, octal 113454).

What is the square root of 38700?

About 196.7232, exactly 30√43.

Is 38700 divisible by 3?

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

What is special about the number 38700?

38700 is a Harshad number: divisible by its digit sum 18.