The number 39780

Q: Is 39780 a prime number?

No. 39780 = 2^2 × 3^2 × 5 × 13 × 17, so it is divisible by 2.

39780 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 13 × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 17, 18, 20, 26, 30 … 39780.

Number

Pick any whole number from 1 to 100,000.

39780 = 2^{2} \times 3^{2} \times 5 \times 13 \times 17

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How to work it out

1
What is special about 39780: a happy number: repeatedly adding the squares of its digits reaches 1.
2
39780 is composite. Its prime factorisation is
$39780 = 2^{2} \times 3^{2} \times 5 \times 13 \times 17$
3
The divisors add up to 137592; without 39780 itself that is 97812, so 39780 is abundant (97812 is more than 39780). Euler's totient φ(39780) = 9216 numbers up to 39780 share no factor with it.
4
The digits of 39780 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 75 steps to reach 1.

LaTeX source of the formulas on this page

\[ 39780 = 2^{2} \times 3^{2} \times 5 \times 13 \times 17 \]

39780 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	137592
Euler totient φ(n)	9216
Square	1582448400
Cube	62949797352000
Square root	199.449242 (= 6√1105)
Digit sum / digital root	27 / 9
Collatz steps to 1	75
Scientific notation	3.978 × $10^{4}$

39780 in other forms

Form	Value
In words	thirty-nine thousand seven hundred and eighty
Binary (base 2)	1001101101100100
Octal (base 8)	115544
Hexadecimal (base 16)	9B64
Base 3	2000120100
As time	39780 seconds = 11 h 3 min 0 s

Is 39780 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (39780 ÷ 2 = 19890)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (39780 ÷ 3 = 13260)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (39780 ÷ 4 = 9945)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (39780 ÷ 5 = 7956)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (39780 ÷ 6 = 6630)	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	Yes (39780 ÷ 9 = 4420)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (39780 ÷ 10 = 3978)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 4)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (39780 ÷ 12 = 3315)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 39780 a prime number?

No. 39780 = $2^{2}$ × $3^{2}$ × 5 × 13 × 17, so it is divisible by 2.

What are the factors of 39780?

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 17, 18, 20, 26, 30, 34, 36, 39, 45, 51, 52, 60, 65, 68, 78, 85, 90, 102, 117, 130, 153, 156, 170, 180, 195, 204, 221, 234, 255, 260, 306, 340, 390, 442, 468, 510, 585, 612, 663, 765, 780, 884, 1020, 1105, 1170, 1326, 1530, 1989, 2210, 2340, 2652, 3060, 3315, 3978, 4420, 6630, 7956, 9945, 13260, 19890, 39780.

What is 39780 in binary?

1001101101100100 (hexadecimal 9B64, octal 115544).

What is the square root of 39780?

About 199.4492, exactly 6√1105.

Is 39780 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 39780?

39780 is a happy number: repeatedly adding the squares of its digits reaches 1.