The number 29400

Q: Is 29400 a prime number?

No. 29400 = 2^3 × 3 × 5^2 × 7^2, so it is divisible by 2.

29400 is a composite number with 72 divisors. Its prime factorisation is $2^{3}$ × 3 × $5^{2}$ × $7^{2}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25 … 29400.

Number

Pick any whole number from 1 to 100,000.

29400 = 2^{3} \times 3 \times 5^{2} \times 7^{2}

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How to work it out

1
What is special about 29400: a Harshad number: divisible by its digit sum 15.
2
29400 is composite. Its prime factorisation is
$29400 = 2^{3} \times 3 \times 5^{2} \times 7^{2}$
3
The divisors add up to 106020; without 29400 itself that is 76620, so 29400 is abundant (76620 is more than 29400). Euler's totient φ(29400) = 6720 numbers up to 29400 share no factor with it.
4
The digits of 29400 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 103 steps to reach 1.

LaTeX source of the formulas on this page

\[ 29400 = 2^{3} \times 3 \times 5^{2} \times 7^{2} \]

29400 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	106020
Euler totient φ(n)	6720
Square	864360000
Cube	25412184000000
Square root	171.464282 (= 70√6)
Digit sum / digital root	15 / 6
Collatz steps to 1	103
Scientific notation	2.94 × $10^{4}$

29400 in other forms

Form	Value
In words	twenty-nine thousand four hundred
Binary (base 2)	111001011011000
Octal (base 8)	71330
Hexadecimal (base 16)	72D8
Base 3	1111022220
As time	29400 seconds = 8 h 10 min 0 s

Is 29400 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (29400 ÷ 2 = 14700)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (29400 ÷ 3 = 9800)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (29400 ÷ 4 = 7350)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (29400 ÷ 5 = 5880)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (29400 ÷ 6 = 4900)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (29400 ÷ 7 = 4200)	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	Yes (29400 ÷ 8 = 3675)	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	Yes (29400 ÷ 10 = 2940)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (29400 ÷ 12 = 2450)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 29400 a prime number?

No. 29400 = $2^{3}$ × 3 × $5^{2}$ × $7^{2}$ , so it is divisible by 2.

What are the factors of 29400?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 49, 50, 56, 60, 70, 75, 84, 98, 100, 105, 120, 140, 147, 150, 168, 175, 196, 200, 210, 245, 280, 294, 300, 350, 392, 420, 490, 525, 588, 600, 700, 735, 840, 980, 1050, 1176, 1225, 1400, 1470, 1960, 2100, 2450, 2940, 3675, 4200, 4900, 5880, 7350, 9800, 14700, 29400.

What is 29400 in binary?

111001011011000 (hexadecimal 72D8, octal 71330).

What is the square root of 29400?

About 171.4643, exactly 70√6.

Is 29400 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 29400?

29400 is a Harshad number: divisible by its digit sum 15.