The number 84420

Q: Is 84420 a prime number?

No. 84420 = 2^2 × 3^2 × 5 × 7 × 67, so it is divisible by 2.

84420 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 7 × 67. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28 … 84420.

Number

Pick any whole number from 1 to 100,000.

84420 = 2^{2} \times 3^{2} \times 5 \times 7 \times 67

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How to work it out

1
What is special about 84420: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
2
84420 is composite. Its prime factorisation is
$84420 = 2^{2} \times 3^{2} \times 5 \times 7 \times 67$
3
The divisors add up to 297024; without 84420 itself that is 212604, so 84420 is abundant (212604 is more than 84420). Euler's totient φ(84420) = 19008 numbers up to 84420 share no factor with it.
4
The digits of 84420 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 58 steps to reach 1.

LaTeX source of the formulas on this page

\[ 84420 = 2^{2} \times 3^{2} \times 5 \times 7 \times 67 \]

84420 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	297024
Euler totient φ(n)	19008
Square	7126736400
Cube	601639086888000
Square root	290.551200 (= 6√2345)
Digit sum / digital root	18 / 9
Collatz steps to 1	58
Scientific notation	8.442 × $10^{4}$

84420 in other forms

Form	Value
In words	eighty-four thousand four hundred and twenty
Binary (base 2)	10100100111000100
Octal (base 8)	244704
Hexadecimal (base 16)	149C4
Base 3	11021210200
As time	84420 seconds = 23 h 27 min 0 s

Is 84420 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (84420 ÷ 2 = 42210)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (84420 ÷ 3 = 28140)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (84420 ÷ 4 = 21105)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (84420 ÷ 5 = 16884)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (84420 ÷ 6 = 14070)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (84420 ÷ 7 = 12060)	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 (84420 ÷ 9 = 9380)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (84420 ÷ 10 = 8442)	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 (84420 ÷ 12 = 7035)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 84420 a prime number?

No. 84420 = $2^{2}$ × $3^{2}$ × 5 × 7 × 67, so it is divisible by 2.

What are the factors of 84420?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 67, 70, 84, 90, 105, 126, 134, 140, 180, 201, 210, 252, 268, 315, 335, 402, 420, 469, 603, 630, 670, 804, 938, 1005, 1206, 1260, 1340, 1407, 1876, 2010, 2345, 2412, 2814, 3015, 4020, 4221, 4690, 5628, 6030, 7035, 8442, 9380, 12060, 14070, 16884, 21105, 28140, 42210, 84420.

What is 84420 in binary?

10100100111000100 (hexadecimal 149C4, octal 244704).

What is the square root of 84420?

About 290.5512, exactly 6√2345.

Is 84420 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 84420?

84420 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.