The number 78988

Q: Is 78988 a prime number?

No. 78988 = 2^2 × 7^2 × 13 × 31, so it is divisible by 2.

78988 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × $7^{2}$ × 13 × 31. Divisors (36): 1, 2, 4, 7, 13, 14, 26, 28, 31, 49, 52, 62, 91, 98, 124, 182 … 78988.

Number

Pick any whole number from 1 to 100,000.

78988 = 2^{2} \times 7^{2} \times 13 \times 31

Explain it step by step in chat Make a short video of it

How to work it out

1
78988 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
78988 is composite. Its prime factorisation is
$78988 = 2^{2} \times 7^{2} \times 13 \times 31$
3
The divisors add up to 178752; without 78988 itself that is 99764, so 78988 is abundant (99764 is more than 78988). Euler's totient φ(78988) = 30240 numbers up to 78988 share no factor with it.
4
The digits of 78988 add up to 40, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.

LaTeX source of the formulas on this page

\[ 78988 = 2^{2} \times 7^{2} \times 13 \times 31 \]

78988 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	178752
Euler totient φ(n)	30240
Square	6239104144
Cube	492814358126272
Square root	281.048039 (= 14√403)
Digit sum / digital root	40 / 4
Collatz steps to 1	138
Scientific notation	7.8988 × $10^{4}$

78988 in other forms

Form	Value
In words	seventy-eight thousand nine hundred and eighty-eight
Binary (base 2)	10011010010001100
Octal (base 8)	232214
Hexadecimal (base 16)	1348C
Base 3	11000100111
As time	78988 seconds = 21 h 56 min 28 s

Is 78988 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (78988 ÷ 2 = 39494)	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 (78988 ÷ 4 = 19747)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	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 (78988 ÷ 7 = 11284)	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 4)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 8)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	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 78988 a prime number?

No. 78988 = $2^{2}$ × $7^{2}$ × 13 × 31, so it is divisible by 2.

What are the factors of 78988?

1, 2, 4, 7, 13, 14, 26, 28, 31, 49, 52, 62, 91, 98, 124, 182, 196, 217, 364, 403, 434, 637, 806, 868, 1274, 1519, 1612, 2548, 2821, 3038, 5642, 6076, 11284, 19747, 39494, 78988.

What is 78988 in binary?

10011010010001100 (hexadecimal 1348C, octal 232214).

What is the square root of 78988?

About 281.0480, exactly 14√403.

Is 78988 divisible by 3?

No. Its digits add up to 40, which is not a multiple of 3.

What is special about the number 78988?

It is a composite number with 36 divisors.