The number 78400

Q: Is 78400 a prime number?

No. 78400 = 2^6 × 5^2 × 7^2, so it is divisible by 2.

78400 is a perfect square (280²). Its prime factorisation is $2^{6}$ × $5^{2}$ × $7^{2}$ . Divisors (63): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49 … 78400.

Number

Pick any whole number from 1 to 100,000.

78400 = 2^{6} \times 5^{2} \times 7^{2}

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How to work it out

1
What is special about 78400: a perfect square (280²); a happy number: repeatedly adding the squares of its digits reaches 1.
2
78400 is composite. Its prime factorisation is
$78400 = 2^{6} \times 5^{2} \times 7^{2}$
3
The divisors add up to 224409; without 78400 itself that is 146009, so 78400 is abundant (146009 is more than 78400). Euler's totient φ(78400) = 26880 numbers up to 78400 share no factor with it.
4
The digits of 78400 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.

LaTeX source of the formulas on this page

\[ 78400 = 2^{6} \times 5^{2} \times 7^{2} \]

78400 at a glance

Property	Value
Type	composite
Number of divisors	63
Sum of divisors	224409
Euler totient φ(n)	26880
Square	6146560000
Cube	481890304000000
Square root	280
Digit sum / digital root	19 / 1
Collatz steps to 1	138
Scientific notation	7.84 × $10^{4}$
Perfect power	$280^{2}$

78400 in other forms

Form	Value
In words	seventy-eight thousand four hundred
Binary (base 2)	10011001001000000
Octal (base 8)	231100
Hexadecimal (base 16)	13240
Base 3	10222112201
As time	78400 seconds = 21 h 46 min 40 s

Is 78400 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (78400 ÷ 2 = 39200)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 1)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (78400 ÷ 4 = 19600)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (78400 ÷ 5 = 15680)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 4)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (78400 ÷ 7 = 11200)	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 (78400 ÷ 8 = 9800)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 1)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (78400 ÷ 10 = 7840)	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	No (remainder 4)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 78400 a prime number?

No. 78400 = $2^{6}$ × $5^{2}$ × $7^{2}$ , so it is divisible by 2.

What are the factors of 78400?

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49, 50, 56, 64, 70, 80, 98, 100, 112, 140, 160, 175, 196, 200, 224, 245, 280, 320, 350, 392, 400, 448, 490, 560, 700, 784, 800, 980, 1120, 1225, 1400, 1568, 1600, 1960, 2240, 2450, 2800, 3136, 3920, 4900, 5600, 7840, 9800, 11200, 15680, 19600, 39200, 78400.

What is 78400 in binary?

10011001001000000 (hexadecimal 13240, octal 231100).

What is the square root of 78400?

280, because 280 × 280 = 78400.

Is 78400 divisible by 3?

No. Its digits add up to 19, which is not a multiple of 3.

What is special about the number 78400?

78400 is a perfect square (280²); a happy number: repeatedly adding the squares of its digits reaches 1.