The number 56784

Q: Is 56784 a prime number?

No. 56784 = 2^4 × 3 × 7 × 13^2, so it is divisible by 2.

56784 is a composite number with 60 divisors. Its prime factorisation is $2^{4}$ × 3 × 7 × $13^{2}$ . Divisors (60): 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 39 … 56784.

Number

Pick any whole number from 1 to 100,000.

56784 = 2^{4} \times 3 \times 7 \times 13^{2}

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How to work it out

1
What is special about 56784: a happy number: repeatedly adding the squares of its digits reaches 1.
2
56784 is composite. Its prime factorisation is
$56784 = 2^{4} \times 3 \times 7 \times 13^{2}$
3
The divisors add up to 181536; without 56784 itself that is 124752, so 56784 is abundant (124752 is more than 56784). Euler's totient φ(56784) = 14976 numbers up to 56784 share no factor with it.
4
The digits of 56784 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.

LaTeX source of the formulas on this page

\[ 56784 = 2^{4} \times 3 \times 7 \times 13^{2} \]

56784 at a glance

Property	Value
Type	composite
Number of divisors	60
Sum of divisors	181536
Euler totient φ(n)	14976
Square	3224422656
Cube	183095616098304
Square root	238.293936 (= 52√21)
Digit sum / digital root	30 / 3
Collatz steps to 1	60
Scientific notation	5.6784 × $10^{4}$

56784 in other forms

Form	Value
In words	fifty-six thousand seven hundred and eighty-four
Binary (base 2)	1101110111010000
Octal (base 8)	156720
Hexadecimal (base 16)	DDD0
Base 3	2212220010
As time	56784 seconds = 15 h 46 min 24 s

Is 56784 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (56784 ÷ 2 = 28392)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (56784 ÷ 3 = 18928)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (56784 ÷ 4 = 14196)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 4)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (56784 ÷ 6 = 9464)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (56784 ÷ 7 = 8112)	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 (56784 ÷ 8 = 7098)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 4)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (56784 ÷ 12 = 4732)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 56784 a prime number?

No. 56784 = $2^{4}$ × 3 × 7 × $13^{2}$ , so it is divisible by 2.

What are the factors of 56784?

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 39, 42, 48, 52, 56, 78, 84, 91, 104, 112, 156, 168, 169, 182, 208, 273, 312, 336, 338, 364, 507, 546, 624, 676, 728, 1014, 1092, 1183, 1352, 1456, 2028, 2184, 2366, 2704, 3549, 4056, 4368, 4732, 7098, 8112, 9464, 14196, 18928, 28392, 56784.

What is 56784 in binary?

1101110111010000 (hexadecimal DDD0, octal 156720).

What is the square root of 56784?

About 238.2939, exactly 52√21.

Is 56784 divisible by 3?

Yes. Its digits add up to 30, a multiple of 3.

What is special about the number 56784?

56784 is a happy number: repeatedly adding the squares of its digits reaches 1.