The number 84672

Q: Is 84672 a prime number?

No. 84672 = 2^6 × 3^3 × 7^2, so it is divisible by 2.

84672 is a composite number with 84 divisors. Its prime factorisation is $2^{6}$ × $3^{3}$ × $7^{2}$ . Divisors (84): 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28 … 84672.

Number

Pick any whole number from 1 to 100,000.

84672 = 2^{6} \times 3^{3} \times 7^{2}

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How to work it out

1
What is special about 84672: a Harshad number: divisible by its digit sum 27.
2
84672 is composite. Its prime factorisation is
$84672 = 2^{6} \times 3^{3} \times 7^{2}$
3
The divisors add up to 289560; without 84672 itself that is 204888, so 84672 is abundant (204888 is more than 84672). Euler's totient φ(84672) = 24192 numbers up to 84672 share no factor with it.
4
The digits of 84672 add up to 27, 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

\[ 84672 = 2^{6} \times 3^{3} \times 7^{2} \]

84672 at a glance

Property	Value
Type	composite
Number of divisors	84
Sum of divisors	289560
Euler totient φ(n)	24192
Square	7169347584
Cube	607042998632448
Square root	290.984536 (= 168√3)
Digit sum / digital root	27 / 9
Collatz steps to 1	58
Scientific notation	8.4672 × $10^{4}$

84672 in other forms

Form	Value
In words	eighty-four thousand six hundred and seventy-two
Binary (base 2)	10100101011000000
Octal (base 8)	245300
Hexadecimal (base 16)	14AC0
Base 3	11022011000
As time	84672 seconds = 23 h 31 min 12 s

Is 84672 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (84672 ÷ 2 = 42336)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (84672 ÷ 3 = 28224)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (84672 ÷ 4 = 21168)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 2)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (84672 ÷ 6 = 14112)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (84672 ÷ 7 = 12096)	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	Yes (84672 ÷ 8 = 10584)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (84672 ÷ 9 = 9408)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 2)	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 (84672 ÷ 12 = 7056)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 84672 a prime number?

No. 84672 = $2^{6}$ × $3^{3}$ × $7^{2}$ , so it is divisible by 2.

What are the factors of 84672?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 49, 54, 56, 63, 64, 72, 84, 96, 98, 108, 112, 126, 144, 147, 168, 189, 192, 196, 216, 224, 252, 288, 294, 336, 378, 392, 432, 441, 448, 504, 576, 588, 672, 756, 784, 864, 882, 1008, 1176, 1323, 1344, 1512, 1568, 1728, 1764, 2016, 2352, 2646, 3024, 3136, 3528, 4032, 4704, 5292, 6048, 7056, 9408, 10584, 12096, 14112, 21168, 28224, 42336, 84672.

What is 84672 in binary?

10100101011000000 (hexadecimal 14AC0, octal 245300).

What is the square root of 84672?

About 290.9845, exactly 168√3.

Is 84672 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 84672?

84672 is a Harshad number: divisible by its digit sum 27.