The number 29700

Q: Is 29700 a prime number?

No. 29700 = 2^2 × 3^3 × 5^2 × 11, so it is divisible by 2.

29700 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × $5^{2}$ × 11. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 27 … 29700.

Number

Pick any whole number from 1 to 100,000.

29700 = 2^{2} \times 3^{3} \times 5^{2} \times 11

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How to work it out

1
What is special about 29700: a Harshad number: divisible by its digit sum 18.
2
29700 is composite. Its prime factorisation is
$29700 = 2^{2} \times 3^{3} \times 5^{2} \times 11$
3
The divisors add up to 104160; without 29700 itself that is 74460, so 29700 is abundant (74460 is more than 29700). Euler's totient φ(29700) = 7200 numbers up to 29700 share no factor with it.
4
The digits of 29700 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 134 steps to reach 1.

LaTeX source of the formulas on this page

\[ 29700 = 2^{2} \times 3^{3} \times 5^{2} \times 11 \]

29700 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	104160
Euler totient φ(n)	7200
Square	882090000
Cube	26198073000000
Square root	172.336879 (= 30√33)
Digit sum / digital root	18 / 9
Collatz steps to 1	134
Scientific notation	2.97 × $10^{4}$

29700 in other forms

Form	Value
In words	twenty-nine thousand seven hundred
Binary (base 2)	111010000000100
Octal (base 8)	72004
Hexadecimal (base 16)	7404
Base 3	1111202000
As time	29700 seconds = 8 h 15 min 0 s

Is 29700 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (29700 ÷ 2 = 14850)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (29700 ÷ 3 = 9900)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (29700 ÷ 4 = 7425)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (29700 ÷ 5 = 5940)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (29700 ÷ 6 = 4950)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (29700 ÷ 9 = 3300)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (29700 ÷ 10 = 2970)	A number is divisible by 10 if the last digit is 0.
11	Yes (29700 ÷ 11 = 2700)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (29700 ÷ 12 = 2475)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 29700 a prime number?

No. 29700 = $2^{2}$ × $3^{3}$ × $5^{2}$ × 11, so it is divisible by 2.

What are the factors of 29700?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 27, 30, 33, 36, 44, 45, 50, 54, 55, 60, 66, 75, 90, 99, 100, 108, 110, 132, 135, 150, 165, 180, 198, 220, 225, 270, 275, 297, 300, 330, 396, 450, 495, 540, 550, 594, 660, 675, 825, 900, 990, 1100, 1188, 1350, 1485, 1650, 1980, 2475, 2700, 2970, 3300, 4950, 5940, 7425, 9900, 14850, 29700.

What is 29700 in binary?

111010000000100 (hexadecimal 7404, octal 72004).

What is the square root of 29700?

About 172.3369, exactly 30√33.

Is 29700 divisible by 3?

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

What is special about the number 29700?

29700 is a Harshad number: divisible by its digit sum 18.