The number 70500

Q: Is 70500 a prime number?

No. 70500 = 2^2 × 3 × 5^3 × 47, so it is divisible by 2.

70500 is a triangular number: 1 + 2 + … + 375 = 70500. Its prime factorisation is $2^{2}$ × 3 × $5^{3}$ × 47. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 47, 50, 60, 75 … 70500.

Number

Pick any whole number from 1 to 100,000.

70500 = 2^{2} \times 3 \times 5^{3} \times 47

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How to work it out

1
What is special about 70500: a triangular number: 1 + 2 + … + 375 = 70500; a Harshad number: divisible by its digit sum 12.
2
70500 is composite. Its prime factorisation is
$70500 = 2^{2} \times 3 \times 5^{3} \times 47$
3
The divisors add up to 209664; without 70500 itself that is 139164, so 70500 is abundant (139164 is more than 70500). Euler's totient φ(70500) = 18400 numbers up to 70500 share no factor with it.
4
The digits of 70500 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.

LaTeX source of the formulas on this page

\[ 70500 = 2^{2} \times 3 \times 5^{3} \times 47 \]

70500 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	209664
Euler totient φ(n)	18400
Square	4970250000
Cube	350402625000000
Square root	265.518361 (= 10√705)
Digit sum / digital root	12 / 3
Collatz steps to 1	143
Scientific notation	7.05 × $10^{4}$

70500 in other forms

Form	Value
In words	seventy thousand five hundred
Binary (base 2)	10001001101100100
Octal (base 8)	211544
Hexadecimal (base 16)	11364
Base 3	10120201010
As time	70500 seconds = 19 h 35 min 0 s

Is 70500 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (70500 ÷ 2 = 35250)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (70500 ÷ 3 = 23500)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (70500 ÷ 4 = 17625)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (70500 ÷ 5 = 14100)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (70500 ÷ 6 = 11750)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 3)	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 (70500 ÷ 10 = 7050)	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 (70500 ÷ 12 = 5875)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 70500 a prime number?

No. 70500 = $2^{2}$ × 3 × $5^{3}$ × 47, so it is divisible by 2.

What are the factors of 70500?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 47, 50, 60, 75, 94, 100, 125, 141, 150, 188, 235, 250, 282, 300, 375, 470, 500, 564, 705, 750, 940, 1175, 1410, 1500, 2350, 2820, 3525, 4700, 5875, 7050, 11750, 14100, 17625, 23500, 35250, 70500.

What is 70500 in binary?

10001001101100100 (hexadecimal 11364, octal 211544).

What is the square root of 70500?

About 265.5184, exactly 10√705.

Is 70500 divisible by 3?

Yes. Its digits add up to 12, a multiple of 3.

What is special about the number 70500?

70500 is a triangular number: 1 + 2 + … + 375 = 70500; a Harshad number: divisible by its digit sum 12.