The number 90420

Q: Is 90420 a prime number?

No. 90420 = 2^2 × 3 × 5 × 11 × 137, so it is divisible by 2.

90420 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 11 × 137. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55 … 90420.

Number

Pick any whole number from 1 to 100,000.

90420 = 2^{2} \times 3 \times 5 \times 11 \times 137

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How to work it out

1
What is special about 90420: a Harshad number: divisible by its digit sum 15.
2
90420 is composite. Its prime factorisation is
$90420 = 2^{2} \times 3 \times 5 \times 11 \times 137$
3
The divisors add up to 278208; without 90420 itself that is 187788, so 90420 is abundant (187788 is more than 90420). Euler's totient φ(90420) = 21760 numbers up to 90420 share no factor with it.
4
The digits of 90420 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 89 steps to reach 1.

LaTeX source of the formulas on this page

\[ 90420 = 2^{2} \times 3 \times 5 \times 11 \times 137 \]

90420 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	278208
Euler totient φ(n)	21760
Square	8175776400
Cube	739253702088000
Square root	300.699185 (= 2√22605)
Digit sum / digital root	15 / 6
Collatz steps to 1	89
Scientific notation	9.042 × $10^{4}$

90420 in other forms

Form	Value
In words	ninety thousand four hundred and twenty
Binary (base 2)	10110000100110100
Octal (base 8)	260464
Hexadecimal (base 16)	16134
Base 3	11121000220
As time	90420 seconds = 25 h 7 min 0 s

Is 90420 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (90420 ÷ 2 = 45210)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (90420 ÷ 3 = 30140)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (90420 ÷ 4 = 22605)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (90420 ÷ 5 = 18084)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (90420 ÷ 6 = 15070)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 (90420 ÷ 10 = 9042)	A number is divisible by 10 if the last digit is 0.
11	Yes (90420 ÷ 11 = 8220)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (90420 ÷ 12 = 7535)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 90420 a prime number?

No. 90420 = $2^{2}$ × 3 × 5 × 11 × 137, so it is divisible by 2.

What are the factors of 90420?

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 137, 165, 220, 274, 330, 411, 548, 660, 685, 822, 1370, 1507, 1644, 2055, 2740, 3014, 4110, 4521, 6028, 7535, 8220, 9042, 15070, 18084, 22605, 30140, 45210, 90420.

What is 90420 in binary?

10110000100110100 (hexadecimal 16134, octal 260464).

What is the square root of 90420?

About 300.6992, exactly 2√22605.

Is 90420 divisible by 3?

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

What is special about the number 90420?

90420 is a Harshad number: divisible by its digit sum 15.