The number 39900

Q: Is 39900 a prime number?

No. 39900 = 2^2 × 3 × 5^2 × 7 × 19, so it is divisible by 2.

39900 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 7 × 19. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 25, 28 … 39900.

Number

Pick any whole number from 1 to 100,000.

39900 = 2^{2} \times 3 \times 5^{2} \times 7 \times 19

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How to work it out

1
What is special about 39900: a Harshad number: divisible by its digit sum 21.
2
39900 is composite. Its prime factorisation is
$39900 = 2^{2} \times 3 \times 5^{2} \times 7 \times 19$
3
The divisors add up to 138880; without 39900 itself that is 98980, so 39900 is abundant (98980 is more than 39900). Euler's totient φ(39900) = 8640 numbers up to 39900 share no factor with it.
4
The digits of 39900 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 168 steps to reach 1.

LaTeX source of the formulas on this page

\[ 39900 = 2^{2} \times 3 \times 5^{2} \times 7 \times 19 \]

39900 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	138880
Euler totient φ(n)	8640
Square	1592010000
Cube	63521199000000
Square root	199.749844 (= 10√399)
Digit sum / digital root	21 / 3
Collatz steps to 1	168
Scientific notation	3.99 × $10^{4}$

39900 in other forms

Form	Value
In words	thirty-nine thousand nine hundred
Binary (base 2)	1001101111011100
Octal (base 8)	115734
Hexadecimal (base 16)	9BDC
Base 3	2000201210
As time	39900 seconds = 11 h 5 min 0 s

Is 39900 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (39900 ÷ 2 = 19950)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (39900 ÷ 3 = 13300)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (39900 ÷ 4 = 9975)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (39900 ÷ 5 = 7980)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (39900 ÷ 6 = 6650)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (39900 ÷ 7 = 5700)	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 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (39900 ÷ 10 = 3990)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (39900 ÷ 12 = 3325)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 39900 a prime number?

No. 39900 = $2^{2}$ × 3 × $5^{2}$ × 7 × 19, so it is divisible by 2.

What are the factors of 39900?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 25, 28, 30, 35, 38, 42, 50, 57, 60, 70, 75, 76, 84, 95, 100, 105, 114, 133, 140, 150, 175, 190, 210, 228, 266, 285, 300, 350, 380, 399, 420, 475, 525, 532, 570, 665, 700, 798, 950, 1050, 1140, 1330, 1425, 1596, 1900, 1995, 2100, 2660, 2850, 3325, 3990, 5700, 6650, 7980, 9975, 13300, 19950, 39900.

What is 39900 in binary?

1001101111011100 (hexadecimal 9BDC, octal 115734).

What is the square root of 39900?

About 199.7498, exactly 10√399.

Is 39900 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 39900?

39900 is a Harshad number: divisible by its digit sum 21.