The number 30420

Q: Is 30420 a prime number?

No. 30420 = 2^2 × 3^2 × 5 × 13^2, so it is divisible by 2.

30420 is a composite number with 54 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × $13^{2}$ . Divisors (54): 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36 … 30420.

Number

Pick any whole number from 1 to 100,000.

30420 = 2^{2} \times 3^{2} \times 5 \times 13^{2}

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How to work it out

1
What is special about 30420: a Harshad number: divisible by its digit sum 9.
2
30420 is composite. Its prime factorisation is
$30420 = 2^{2} \times 3^{2} \times 5 \times 13^{2}$
3
The divisors add up to 99918; without 30420 itself that is 69498, so 30420 is abundant (69498 is more than 30420). Euler's totient φ(30420) = 7488 numbers up to 30420 share no factor with it.
4
The digits of 30420 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 33 steps to reach 1.

LaTeX source of the formulas on this page

\[ 30420 = 2^{2} \times 3^{2} \times 5 \times 13^{2} \]

30420 at a glance

Property	Value
Type	composite
Number of divisors	54
Sum of divisors	99918
Euler totient φ(n)	7488
Square	925376400
Cube	28149950088000
Square root	174.413302 (= 78√5)
Digit sum / digital root	9 / 9
Collatz steps to 1	33
Scientific notation	3.042 × $10^{4}$

30420 in other forms

Form	Value
In words	thirty thousand four hundred and twenty
Binary (base 2)	111011011010100
Octal (base 8)	73324
Hexadecimal (base 16)	76D4
Base 3	1112201200
As time	30420 seconds = 8 h 27 min 0 s

Is 30420 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (30420 ÷ 2 = 15210)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (30420 ÷ 3 = 10140)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (30420 ÷ 4 = 7605)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (30420 ÷ 5 = 6084)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (30420 ÷ 6 = 5070)	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	No (remainder 4)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (30420 ÷ 9 = 3380)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (30420 ÷ 10 = 3042)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (30420 ÷ 12 = 2535)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 30420 a prime number?

No. 30420 = $2^{2}$ × $3^{2}$ × 5 × $13^{2}$ , so it is divisible by 2.

What are the factors of 30420?

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 169, 180, 195, 234, 260, 338, 390, 468, 507, 585, 676, 780, 845, 1014, 1170, 1521, 1690, 2028, 2340, 2535, 3042, 3380, 5070, 6084, 7605, 10140, 15210, 30420.

What is 30420 in binary?

111011011010100 (hexadecimal 76D4, octal 73324).

What is the square root of 30420?

About 174.4133, exactly 78√5.

Is 30420 divisible by 3?

Yes. Its digits add up to 9, a multiple of 3.

What is special about the number 30420?

30420 is a Harshad number: divisible by its digit sum 9.