The number 77748

Q: Is 77748 a prime number?

No. 77748 = 2^2 × 3 × 11 × 19 × 31, so it is divisible by 2.

77748 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 11 × 19 × 31. Divisors (48): 1, 2, 3, 4, 6, 11, 12, 19, 22, 31, 33, 38, 44, 57, 62, 66 … 77748.

Number

Pick any whole number from 1 to 100,000.

77748 = 2^{2} \times 3 \times 11 \times 19 \times 31

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How to work it out

1
What is special about 77748: a Harshad number: divisible by its digit sum 33.
2
77748 is composite. Its prime factorisation is
$77748 = 2^{2} \times 3 \times 11 \times 19 \times 31$
3
The divisors add up to 215040; without 77748 itself that is 137292, so 77748 is abundant (137292 is more than 77748). Euler's totient φ(77748) = 21600 numbers up to 77748 share no factor with it.
4
The digits of 77748 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77748 = 2^{2} \times 3 \times 11 \times 19 \times 31 \]

77748 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	215040
Euler totient φ(n)	21600
Square	6044751504
Cube	469967339932992
Square root	278.833284 (= 2√19437)
Digit sum / digital root	33 / 6
Collatz steps to 1	125
Scientific notation	7.7748 × $10^{4}$

77748 in other forms

Form	Value
In words	seventy-seven thousand seven hundred and forty-eight
Binary (base 2)	10010111110110100
Octal (base 8)	227664
Hexadecimal (base 16)	12FB4
Base 3	10221122120
As time	77748 seconds = 21 h 35 min 48 s

Is 77748 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77748 ÷ 2 = 38874)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77748 ÷ 3 = 25916)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77748 ÷ 4 = 19437)	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	Yes (77748 ÷ 6 = 12958)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 6)	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 6)	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	Yes (77748 ÷ 11 = 7068)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (77748 ÷ 12 = 6479)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77748 a prime number?

No. 77748 = $2^{2}$ × 3 × 11 × 19 × 31, so it is divisible by 2.

What are the factors of 77748?

1, 2, 3, 4, 6, 11, 12, 19, 22, 31, 33, 38, 44, 57, 62, 66, 76, 93, 114, 124, 132, 186, 209, 228, 341, 372, 418, 589, 627, 682, 836, 1023, 1178, 1254, 1364, 1767, 2046, 2356, 2508, 3534, 4092, 6479, 7068, 12958, 19437, 25916, 38874, 77748.

What is 77748 in binary?

10010111110110100 (hexadecimal 12FB4, octal 227664).

What is the square root of 77748?

About 278.8333, exactly 2√19437.

Is 77748 divisible by 3?

Yes. Its digits add up to 33, a multiple of 3.

What is special about the number 77748?

77748 is a Harshad number: divisible by its digit sum 33.