The number 96900

Q: Is 96900 a prime number?

No. 96900 = 2^2 × 3 × 5^2 × 17 × 19, so it is divisible by 2.

96900 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 17 × 19. Divisors (72): 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 19, 20, 25, 30, 34, 38 … 96900.

Number

Pick any whole number from 1 to 100,000.

96900 = 2^{2} \times 3 \times 5^{2} \times 17 \times 19

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How to work it out

1
96900 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
96900 is composite. Its prime factorisation is
$96900 = 2^{2} \times 3 \times 5^{2} \times 17 \times 19$
3
The divisors add up to 312480; without 96900 itself that is 215580, so 96900 is abundant (215580 is more than 96900). Euler's totient φ(96900) = 23040 numbers up to 96900 share no factor with it.
4
The digits of 96900 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 71 steps to reach 1.

LaTeX source of the formulas on this page

\[ 96900 = 2^{2} \times 3 \times 5^{2} \times 17 \times 19 \]

96900 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	312480
Euler totient φ(n)	23040
Square	9389610000
Cube	909853209000000
Square root	311.287648 (= 10√969)
Digit sum / digital root	24 / 6
Collatz steps to 1	71
Scientific notation	9.69 × $10^{4}$

96900 in other forms

Form	Value
In words	ninety-six thousand nine hundred
Binary (base 2)	10111101010000100
Octal (base 8)	275204
Hexadecimal (base 16)	17A84
Base 3	11220220220
As time	96900 seconds = 26 h 55 min 0 s

Is 96900 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (96900 ÷ 2 = 48450)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (96900 ÷ 3 = 32300)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (96900 ÷ 4 = 24225)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (96900 ÷ 5 = 19380)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (96900 ÷ 6 = 16150)	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	No (remainder 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (96900 ÷ 10 = 9690)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 1)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (96900 ÷ 12 = 8075)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 96900 a prime number?

No. 96900 = $2^{2}$ × 3 × $5^{2}$ × 17 × 19, so it is divisible by 2.

What are the factors of 96900?

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 19, 20, 25, 30, 34, 38, 50, 51, 57, 60, 68, 75, 76, 85, 95, 100, 102, 114, 150, 170, 190, 204, 228, 255, 285, 300, 323, 340, 380, 425, 475, 510, 570, 646, 850, 950, 969, 1020, 1140, 1275, 1292, 1425, 1615, 1700, 1900, 1938, 2550, 2850, 3230, 3876, 4845, 5100, 5700, 6460, 8075, 9690, 16150, 19380, 24225, 32300, 48450, 96900.

What is 96900 in binary?

10111101010000100 (hexadecimal 17A84, octal 275204).

What is the square root of 96900?

About 311.2876, exactly 10√969.

Is 96900 divisible by 3?

Yes. Its digits add up to 24, a multiple of 3.

What is special about the number 96900?

It is a composite number with 72 divisors.