The number 21420

Q: Is 21420 a prime number?

No. 21420 = 2^2 × 3^2 × 5 × 7 × 17, so it is divisible by 2.

21420 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 7 × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21 … 21420.

Number

Pick any whole number from 1 to 100,000.

21420 = 2^{2} \times 3^{2} \times 5 \times 7 \times 17

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How to work it out

1
What is special about 21420: a Harshad number: divisible by its digit sum 9.
2
21420 is composite. Its prime factorisation is
$21420 = 2^{2} \times 3^{2} \times 5 \times 7 \times 17$
3
The divisors add up to 78624; without 21420 itself that is 57204, so 21420 is abundant (57204 is more than 21420). Euler's totient φ(21420) = 4608 numbers up to 21420 share no factor with it.
4
The digits of 21420 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 100 steps to reach 1.

LaTeX source of the formulas on this page

\[ 21420 = 2^{2} \times 3^{2} \times 5 \times 7 \times 17 \]

21420 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	78624
Euler totient φ(n)	4608
Square	458816400
Cube	9827847288000
Square root	146.355731 (= 6√595)
Digit sum / digital root	9 / 9
Collatz steps to 1	100
Scientific notation	2.142 × $10^{4}$

21420 in other forms

Form	Value
In words	twenty-one thousand four hundred and twenty
Binary (base 2)	101001110101100
Octal (base 8)	51654
Hexadecimal (base 16)	53AC
Base 3	1002101100
As time	21420 seconds = 5 h 57 min 0 s

Is 21420 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (21420 ÷ 2 = 10710)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (21420 ÷ 3 = 7140)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (21420 ÷ 4 = 5355)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (21420 ÷ 5 = 4284)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (21420 ÷ 6 = 3570)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (21420 ÷ 7 = 3060)	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 (21420 ÷ 9 = 2380)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (21420 ÷ 10 = 2142)	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 (21420 ÷ 12 = 1785)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 21420 a prime number?

No. 21420 = $2^{2}$ × $3^{2}$ × 5 × 7 × 17, so it is divisible by 2.

What are the factors of 21420?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 28, 30, 34, 35, 36, 42, 45, 51, 60, 63, 68, 70, 84, 85, 90, 102, 105, 119, 126, 140, 153, 170, 180, 204, 210, 238, 252, 255, 306, 315, 340, 357, 420, 476, 510, 595, 612, 630, 714, 765, 1020, 1071, 1190, 1260, 1428, 1530, 1785, 2142, 2380, 3060, 3570, 4284, 5355, 7140, 10710, 21420.

What is 21420 in binary?

101001110101100 (hexadecimal 53AC, octal 51654).

What is the square root of 21420?

About 146.3557, exactly 6√595.

Is 21420 divisible by 3?

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

What is special about the number 21420?

21420 is a Harshad number: divisible by its digit sum 9.