The number 40950

Q: Is 40950 a prime number?

No. 40950 = 2 × 3^2 × 5^2 × 7 × 13, so it is divisible by 2.

40950 is a composite number with 72 divisors. Its prime factorisation is 2 × $3^{2}$ × $5^{2}$ × 7 × 13. Divisors (72): 1, 2, 3, 5, 6, 7, 9, 10, 13, 14, 15, 18, 21, 25, 26, 30 … 40950.

Number

Pick any whole number from 1 to 100,000.

40950 = 2 \times 3^{2} \times 5^{2} \times 7 \times 13

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How to work it out

1
What is special about 40950: a Harshad number: divisible by its digit sum 18.
2
40950 is composite. Its prime factorisation is
$40950 = 2 \times 3^{2} \times 5^{2} \times 7 \times 13$
3
The divisors add up to 135408; without 40950 itself that is 94458, so 40950 is abundant (94458 is more than 40950). Euler's totient φ(40950) = 8640 numbers up to 40950 share no factor with it.
4
The digits of 40950 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.

LaTeX source of the formulas on this page

\[ 40950 = 2 \times 3^{2} \times 5^{2} \times 7 \times 13 \]

40950 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	135408
Euler totient φ(n)	8640
Square	1676902500
Cube	68669157375000
Square root	202.361063 (= 15√182)
Digit sum / digital root	18 / 9
Collatz steps to 1	62
Scientific notation	4.095 × $10^{4}$

40950 in other forms

Form	Value
In words	forty thousand nine hundred and fifty
Binary (base 2)	1001111111110110
Octal (base 8)	117766
Hexadecimal (base 16)	9FF6
Base 3	2002011200
As time	40950 seconds = 11 h 22 min 30 s

Is 40950 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (40950 ÷ 2 = 20475)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (40950 ÷ 3 = 13650)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	No (remainder 2)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (40950 ÷ 5 = 8190)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (40950 ÷ 6 = 6825)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (40950 ÷ 7 = 5850)	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 6)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (40950 ÷ 9 = 4550)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (40950 ÷ 10 = 4095)	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 6)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 40950 a prime number?

No. 40950 = 2 × $3^{2}$ × $5^{2}$ × 7 × 13, so it is divisible by 2.

What are the factors of 40950?

1, 2, 3, 5, 6, 7, 9, 10, 13, 14, 15, 18, 21, 25, 26, 30, 35, 39, 42, 45, 50, 63, 65, 70, 75, 78, 90, 91, 105, 117, 126, 130, 150, 175, 182, 195, 210, 225, 234, 273, 315, 325, 350, 390, 450, 455, 525, 546, 585, 630, 650, 819, 910, 975, 1050, 1170, 1365, 1575, 1638, 1950, 2275, 2730, 2925, 3150, 4095, 4550, 5850, 6825, 8190, 13650, 20475, 40950.

What is 40950 in binary?

1001111111110110 (hexadecimal 9FF6, octal 117766).

What is the square root of 40950?

About 202.3611, exactly 15√182.

Is 40950 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 40950?

40950 is a Harshad number: divisible by its digit sum 18.