The number 49140

Q: Is 49140 a prime number?

No. 49140 = 2^2 × 3^3 × 5 × 7 × 13, so it is divisible by 2.

49140 is a composite number with 96 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × 5 × 7 × 13. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 18, 20, 21 … 49140.

Number

Pick any whole number from 1 to 100,000.

49140 = 2^{2} \times 3^{3} \times 5 \times 7 \times 13

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How to work it out

1
What is special about 49140: a Harshad number: divisible by its digit sum 18.
2
49140 is composite. Its prime factorisation is
$49140 = 2^{2} \times 3^{3} \times 5 \times 7 \times 13$
3
The divisors add up to 188160; without 49140 itself that is 139020, so 49140 is abundant (139020 is more than 49140). Euler's totient φ(49140) = 10368 numbers up to 49140 share no factor with it.
4
The digits of 49140 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 158 steps to reach 1.

LaTeX source of the formulas on this page

\[ 49140 = 2^{2} \times 3^{3} \times 5 \times 7 \times 13 \]

49140 at a glance

Property	Value
Type	composite
Number of divisors	96
Sum of divisors	188160
Euler totient φ(n)	10368
Square	2414739600
Cube	118660303944000
Square root	221.675438 (= 6√1365)
Digit sum / digital root	18 / 9
Collatz steps to 1	158
Scientific notation	4.914 × $10^{4}$

49140 in other forms

Form	Value
In words	forty-nine thousand one hundred and forty
Binary (base 2)	1011111111110100
Octal (base 8)	137764
Hexadecimal (base 16)	BFF4
Base 3	2111102000
As time	49140 seconds = 13 h 39 min 0 s

Is 49140 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (49140 ÷ 2 = 24570)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (49140 ÷ 3 = 16380)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (49140 ÷ 4 = 12285)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (49140 ÷ 5 = 9828)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (49140 ÷ 6 = 8190)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (49140 ÷ 7 = 7020)	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 (49140 ÷ 9 = 5460)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (49140 ÷ 10 = 4914)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (49140 ÷ 12 = 4095)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 49140 a prime number?

No. 49140 = $2^{2}$ × $3^{3}$ × 5 × 7 × 13, so it is divisible by 2.

What are the factors of 49140?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 18, 20, 21, 26, 27, 28, 30, 35, 36, 39, 42, 45, 52, 54, 60, 63, 65, 70, 78, 84, 90, 91, 105, 108, 117, 126, 130, 135, 140, 156, 180, 182, 189, 195, 210, 234, 252, 260, 270, 273, 315, 351, 364, 378, 390, 420, 455, 468, 540, 546, 585, 630, 702, 756, 780, 819, 910, 945, 1092, 1170, 1260, 1365, 1404, 1638, 1755, 1820, 1890, 2340, 2457, 2730, 3276, 3510, 3780, 4095, 4914, 5460, 7020, 8190, 9828, 12285, 16380, 24570, 49140.

What is 49140 in binary?

1011111111110100 (hexadecimal BFF4, octal 137764).

What is the square root of 49140?

About 221.6754, exactly 6√1365.

Is 49140 divisible by 3?

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

What is special about the number 49140?

49140 is a Harshad number: divisible by its digit sum 18.