The number 40920

Q: Is 40920 a prime number?

No. 40920 = 2^3 × 3 × 5 × 11 × 31, so it is divisible by 2.

40920 is a composite number with 64 divisors. Its prime factorisation is $2^{3}$ × 3 × 5 × 11 × 31. Divisors (64): 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 31 … 40920.

Number

Pick any whole number from 1 to 100,000.

40920 = 2^{3} \times 3 \times 5 \times 11 \times 31

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How to work it out

1
What is special about 40920: a Harshad number: divisible by its digit sum 15.
2
40920 is composite. Its prime factorisation is
$40920 = 2^{3} \times 3 \times 5 \times 11 \times 31$
3
The divisors add up to 138240; without 40920 itself that is 97320, so 40920 is abundant (97320 is more than 40920). Euler's totient φ(40920) = 9600 numbers up to 40920 share no factor with it.
4
The digits of 40920 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.

LaTeX source of the formulas on this page

\[ 40920 = 2^{3} \times 3 \times 5 \times 11 \times 31 \]

40920 at a glance

Property	Value
Type	composite
Number of divisors	64
Sum of divisors	138240
Euler totient φ(n)	9600
Square	1674446400
Cube	68518346688000
Square root	202.286925 (= 2√10230)
Digit sum / digital root	15 / 6
Collatz steps to 1	62
Scientific notation	4.092 × $10^{4}$

40920 in other forms

Form	Value
In words	forty thousand nine hundred and twenty
Binary (base 2)	1001111111011000
Octal (base 8)	117730
Hexadecimal (base 16)	9FD8
Base 3	2002010120
As time	40920 seconds = 11 h 22 min 0 s

Is 40920 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (40920 ÷ 2 = 20460)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (40920 ÷ 3 = 13640)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (40920 ÷ 4 = 10230)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (40920 ÷ 5 = 8184)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (40920 ÷ 6 = 6820)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 5)	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	Yes (40920 ÷ 8 = 5115)	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	Yes (40920 ÷ 10 = 4092)	A number is divisible by 10 if the last digit is 0.
11	Yes (40920 ÷ 11 = 3720)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (40920 ÷ 12 = 3410)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 40920 a prime number?

No. 40920 = $2^{3}$ × 3 × 5 × 11 × 31, so it is divisible by 2.

What are the factors of 40920?

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 31, 33, 40, 44, 55, 60, 62, 66, 88, 93, 110, 120, 124, 132, 155, 165, 186, 220, 248, 264, 310, 330, 341, 372, 440, 465, 620, 660, 682, 744, 930, 1023, 1240, 1320, 1364, 1705, 1860, 2046, 2728, 3410, 3720, 4092, 5115, 6820, 8184, 10230, 13640, 20460, 40920.

What is 40920 in binary?

1001111111011000 (hexadecimal 9FD8, octal 117730).

What is the square root of 40920?

About 202.2869, exactly 2√10230.

Is 40920 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 40920?

40920 is a Harshad number: divisible by its digit sum 15.