The number 38220

Q: Is 38220 a prime number?

No. 38220 = 2^2 × 3 × 5 × 7^2 × 13, so it is divisible by 2.

38220 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × $7^{2}$ × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28 … 38220.

Number

Pick any whole number from 1 to 100,000.

38220 = 2^{2} \times 3 \times 5 \times 7^{2} \times 13

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How to work it out

1
What is special about 38220: a Harshad number: divisible by its digit sum 15.
2
38220 is composite. Its prime factorisation is
$38220 = 2^{2} \times 3 \times 5 \times 7^{2} \times 13$
3
The divisors add up to 134064; without 38220 itself that is 95844, so 38220 is abundant (95844 is more than 38220). Euler's totient φ(38220) = 8064 numbers up to 38220 share no factor with it.
4
The digits of 38220 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 106 steps to reach 1.

LaTeX source of the formulas on this page

\[ 38220 = 2^{2} \times 3 \times 5 \times 7^{2} \times 13 \]

38220 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	134064
Euler totient φ(n)	8064
Square	1460768400
Cube	55830568248000
Square root	195.499361 (= 14√195)
Digit sum / digital root	15 / 6
Collatz steps to 1	106
Scientific notation	3.822 × $10^{4}$

38220 in other forms

Form	Value
In words	thirty-eight thousand two hundred and twenty
Binary (base 2)	1001010101001100
Octal (base 8)	112514
Hexadecimal (base 16)	954C
Base 3	1221102120
As time	38220 seconds = 10 h 37 min 0 s

Is 38220 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (38220 ÷ 2 = 19110)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (38220 ÷ 3 = 12740)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (38220 ÷ 4 = 9555)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (38220 ÷ 5 = 7644)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (38220 ÷ 6 = 6370)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (38220 ÷ 7 = 5460)	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 (38220 ÷ 10 = 3822)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 6)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (38220 ÷ 12 = 3185)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 38220 a prime number?

No. 38220 = $2^{2}$ × 3 × 5 × $7^{2}$ × 13, so it is divisible by 2.

What are the factors of 38220?

1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 49, 52, 60, 65, 70, 78, 84, 91, 98, 105, 130, 140, 147, 156, 182, 195, 196, 210, 245, 260, 273, 294, 364, 390, 420, 455, 490, 546, 588, 637, 735, 780, 910, 980, 1092, 1274, 1365, 1470, 1820, 1911, 2548, 2730, 2940, 3185, 3822, 5460, 6370, 7644, 9555, 12740, 19110, 38220.

What is 38220 in binary?

1001010101001100 (hexadecimal 954C, octal 112514).

What is the square root of 38220?

About 195.4994, exactly 14√195.

Is 38220 divisible by 3?

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

What is special about the number 38220?

38220 is a Harshad number: divisible by its digit sum 15.