The number 77700

Q: Is 77700 a prime number?

No. 77700 = 2^2 × 3 × 5^2 × 7 × 37, so it is divisible by 2.

77700 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 7 × 37. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30 … 77700.

Number

Pick any whole number from 1 to 100,000.

77700 = 2^{2} \times 3 \times 5^{2} \times 7 \times 37

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How to work it out

1
What is special about 77700: a Harshad number: divisible by its digit sum 21.
2
77700 is composite. Its prime factorisation is
$77700 = 2^{2} \times 3 \times 5^{2} \times 7 \times 37$
3
The divisors add up to 263872; without 77700 itself that is 186172, so 77700 is abundant (186172 is more than 77700). Euler's totient φ(77700) = 17280 numbers up to 77700 share no factor with it.
4
The digits of 77700 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77700 = 2^{2} \times 3 \times 5^{2} \times 7 \times 37 \]

77700 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	263872
Euler totient φ(n)	17280
Square	6037290000
Cube	469097433000000
Square root	278.747197 (= 10√777)
Digit sum / digital root	21 / 3
Collatz steps to 1	63
Scientific notation	7.77 × $10^{4}$

77700 in other forms

Form	Value
In words	seventy-seven thousand seven hundred
Binary (base 2)	10010111110000100
Octal (base 8)	227604
Hexadecimal (base 16)	12F84
Base 3	10221120210
As time	77700 seconds = 21 h 35 min 0 s

Is 77700 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77700 ÷ 2 = 38850)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77700 ÷ 3 = 25900)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77700 ÷ 4 = 19425)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (77700 ÷ 5 = 15540)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (77700 ÷ 6 = 12950)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (77700 ÷ 7 = 11100)	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 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (77700 ÷ 10 = 7770)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 7)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (77700 ÷ 12 = 6475)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77700 a prime number?

No. 77700 = $2^{2}$ × 3 × $5^{2}$ × 7 × 37, so it is divisible by 2.

What are the factors of 77700?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 37, 42, 50, 60, 70, 74, 75, 84, 100, 105, 111, 140, 148, 150, 175, 185, 210, 222, 259, 300, 350, 370, 420, 444, 518, 525, 555, 700, 740, 777, 925, 1036, 1050, 1110, 1295, 1554, 1850, 2100, 2220, 2590, 2775, 3108, 3700, 3885, 5180, 5550, 6475, 7770, 11100, 12950, 15540, 19425, 25900, 38850, 77700.

What is 77700 in binary?

10010111110000100 (hexadecimal 12F84, octal 227604).

What is the square root of 77700?

About 278.7472, exactly 10√777.

Is 77700 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 77700?

77700 is a Harshad number: divisible by its digit sum 21.