The number 78100

Q: Is 78100 a prime number?

No. 78100 = 2^2 × 5^2 × 11 × 71, so it is divisible by 2.

78100 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × $5^{2}$ × 11 × 71. Divisors (36): 1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 71, 100, 110, 142 … 78100.

Number

Pick any whole number from 1 to 100,000.

78100 = 2^{2} \times 5^{2} \times 11 \times 71

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How to work it out

1
78100 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
78100 is composite. Its prime factorisation is
$78100 = 2^{2} \times 5^{2} \times 11 \times 71$
3
The divisors add up to 187488; without 78100 itself that is 109388, so 78100 is abundant (109388 is more than 78100). Euler's totient φ(78100) = 28000 numbers up to 78100 share no factor with it.
4
The digits of 78100 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.

LaTeX source of the formulas on this page

\[ 78100 = 2^{2} \times 5^{2} \times 11 \times 71 \]

78100 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	187488
Euler totient φ(n)	28000
Square	6099610000
Cube	476379541000000
Square root	279.463772 (= 10√781)
Digit sum / digital root	16 / 7
Collatz steps to 1	138
Scientific notation	7.81 × $10^{4}$

78100 in other forms

Form	Value
In words	seventy-eight thousand one hundred
Binary (base 2)	10011000100010100
Octal (base 8)	230424
Hexadecimal (base 16)	13114
Base 3	10222010121
As time	78100 seconds = 21 h 41 min 40 s

Is 78100 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (78100 ÷ 2 = 39050)	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 (78100 ÷ 4 = 19525)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (78100 ÷ 5 = 15620)	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	No (remainder 1)	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	No (remainder 7)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (78100 ÷ 10 = 7810)	A number is divisible by 10 if the last digit is 0.
11	Yes (78100 ÷ 11 = 7100)	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 78100 a prime number?

No. 78100 = $2^{2}$ × $5^{2}$ × 11 × 71, so it is divisible by 2.

What are the factors of 78100?

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 71, 100, 110, 142, 220, 275, 284, 355, 550, 710, 781, 1100, 1420, 1562, 1775, 3124, 3550, 3905, 7100, 7810, 15620, 19525, 39050, 78100.

What is 78100 in binary?

10011000100010100 (hexadecimal 13114, octal 230424).

What is the square root of 78100?

About 279.4638, exactly 10√781.

Is 78100 divisible by 3?

No. Its digits add up to 16, which is not a multiple of 3.

What is special about the number 78100?

It is a composite number with 36 divisors.