The number 76200

Q: Is 76200 a prime number?

No. 76200 = 2^3 × 3 × 5^2 × 127, so it is divisible by 2.

76200 is a composite number with 48 divisors. Its prime factorisation is $2^{3}$ × 3 × $5^{2}$ × 127. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50 … 76200.

Number

Pick any whole number from 1 to 100,000.

76200 = 2^{3} \times 3 \times 5^{2} \times 127

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How to work it out

1
What is special about 76200: a Harshad number: divisible by its digit sum 15.
2
76200 is composite. Its prime factorisation is
$76200 = 2^{3} \times 3 \times 5^{2} \times 127$
3
The divisors add up to 238080; without 76200 itself that is 161880, so 76200 is abundant (161880 is more than 76200). Euler's totient φ(76200) = 20160 numbers up to 76200 share no factor with it.
4
The digits of 76200 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 81 steps to reach 1.

LaTeX source of the formulas on this page

\[ 76200 = 2^{3} \times 3 \times 5^{2} \times 127 \]

76200 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	238080
Euler totient φ(n)	20160
Square	5806440000
Cube	442450728000000
Square root	276.043475 (= 10√762)
Digit sum / digital root	15 / 6
Collatz steps to 1	81
Scientific notation	7.62 × $10^{4}$

76200 in other forms

Form	Value
In words	seventy-six thousand two hundred
Binary (base 2)	10010100110101000
Octal (base 8)	224650
Hexadecimal (base 16)	129A8
Base 3	10212112020
As time	76200 seconds = 21 h 10 min 0 s

Is 76200 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (76200 ÷ 2 = 38100)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (76200 ÷ 3 = 25400)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (76200 ÷ 4 = 19050)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (76200 ÷ 5 = 15240)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (76200 ÷ 6 = 12700)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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 (76200 ÷ 8 = 9525)	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 (76200 ÷ 10 = 7620)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (76200 ÷ 12 = 6350)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 76200 a prime number?

No. 76200 = $2^{3}$ × 3 × $5^{2}$ × 127, so it is divisible by 2.

What are the factors of 76200?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 127, 150, 200, 254, 300, 381, 508, 600, 635, 762, 1016, 1270, 1524, 1905, 2540, 3048, 3175, 3810, 5080, 6350, 7620, 9525, 12700, 15240, 19050, 25400, 38100, 76200.

What is 76200 in binary?

10010100110101000 (hexadecimal 129A8, octal 224650).

What is the square root of 76200?

About 276.0435, exactly 10√762.

Is 76200 divisible by 3?

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

What is special about the number 76200?

76200 is a Harshad number: divisible by its digit sum 15.