The number 98000

Q: Is 98000 a prime number?

No. 98000 = 2^4 × 5^3 × 7^2, so it is divisible by 2.

98000 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × $5^{3}$ × $7^{2}$ . Divisors (60): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 49, 50 … 98000.

Number

Pick any whole number from 1 to 100,000.

98000 = 2^{4} \times 5^{3} \times 7^{2}

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How to work it out

1
98000 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
98000 is composite. Its prime factorisation is
$98000 = 2^{4} \times 5^{3} \times 7^{2}$
3
The divisors add up to 275652; without 98000 itself that is 177652, so 98000 is abundant (177652 is more than 98000). Euler's totient φ(98000) = 33600 numbers up to 98000 share no factor with it.
4
The digits of 98000 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 66 steps to reach 1.

LaTeX source of the formulas on this page

\[ 98000 = 2^{4} \times 5^{3} \times 7^{2} \]

98000 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	275652
Euler totient φ(n)	33600
Square	9604000000
Cube	941192000000000
Square root	313.049517 (= 140√5)
Digit sum / digital root	17 / 8
Collatz steps to 1	66
Scientific notation	9.8 × $10^{4}$

98000 in other forms

Form	Value
In words	ninety-eight thousand
Binary (base 2)	10111111011010000
Octal (base 8)	277320
Hexadecimal (base 16)	17ED0
Base 3	11222102122
As time	98000 seconds = 27 h 13 min 20 s

Is 98000 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (98000 ÷ 2 = 49000)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (98000 ÷ 4 = 24500)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (98000 ÷ 5 = 19600)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 2)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (98000 ÷ 7 = 14000)	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 (98000 ÷ 8 = 12250)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 8)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (98000 ÷ 10 = 9800)	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	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 98000 a prime number?

No. 98000 = $2^{4}$ × $5^{3}$ × $7^{2}$ , so it is divisible by 2.

What are the factors of 98000?

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 49, 50, 56, 70, 80, 98, 100, 112, 125, 140, 175, 196, 200, 245, 250, 280, 350, 392, 400, 490, 500, 560, 700, 784, 875, 980, 1000, 1225, 1400, 1750, 1960, 2000, 2450, 2800, 3500, 3920, 4900, 6125, 7000, 9800, 12250, 14000, 19600, 24500, 49000, 98000.

What is 98000 in binary?

10111111011010000 (hexadecimal 17ED0, octal 277320).

What is the square root of 98000?

About 313.0495, exactly 140√5.

Is 98000 divisible by 3?

No. Its digits add up to 17, which is not a multiple of 3.

What is special about the number 98000?

It is a composite number with 60 divisors.