The number 49980

Q: Is 49980 a prime number?

No. 49980 = 2^2 × 3 × 5 × 7^2 × 17, so it is divisible by 2.

49980 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × $7^{2}$ × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30 … 49980.

Number

Pick any whole number from 1 to 100,000.

49980 = 2^{2} \times 3 \times 5 \times 7^{2} \times 17

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 49980: a Harshad number: divisible by its digit sum 30.
2
49980 is composite. Its prime factorisation is
$49980 = 2^{2} \times 3 \times 5 \times 7^{2} \times 17$
3
The divisors add up to 172368; without 49980 itself that is 122388, so 49980 is abundant (122388 is more than 49980). Euler's totient φ(49980) = 10752 numbers up to 49980 share no factor with it.
4
The digits of 49980 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 189 steps to reach 1.

LaTeX source of the formulas on this page

\[ 49980 = 2^{2} \times 3 \times 5 \times 7^{2} \times 17 \]

49980 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	172368
Euler totient φ(n)	10752
Square	2498000400
Cube	124850059992000
Square root	223.562072 (= 14√255)
Digit sum / digital root	30 / 3
Collatz steps to 1	189
Scientific notation	4.998 × $10^{4}$

49980 in other forms

Form	Value
In words	forty-nine thousand nine hundred and eighty
Binary (base 2)	1100001100111100
Octal (base 8)	141474
Hexadecimal (base 16)	C33C
Base 3	2112120010
As time	49980 seconds = 13 h 53 min 0 s

Is 49980 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (49980 ÷ 2 = 24990)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (49980 ÷ 3 = 16660)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (49980 ÷ 4 = 12495)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (49980 ÷ 5 = 9996)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (49980 ÷ 6 = 8330)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (49980 ÷ 7 = 7140)	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 (49980 ÷ 10 = 4998)	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 (49980 ÷ 12 = 4165)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 49980 a prime number?

No. 49980 = $2^{2}$ × 3 × 5 × $7^{2}$ × 17, so it is divisible by 2.

What are the factors of 49980?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 49, 51, 60, 68, 70, 84, 85, 98, 102, 105, 119, 140, 147, 170, 196, 204, 210, 238, 245, 255, 294, 340, 357, 420, 476, 490, 510, 588, 595, 714, 735, 833, 980, 1020, 1190, 1428, 1470, 1666, 1785, 2380, 2499, 2940, 3332, 3570, 4165, 4998, 7140, 8330, 9996, 12495, 16660, 24990, 49980.

What is 49980 in binary?

1100001100111100 (hexadecimal C33C, octal 141474).

What is the square root of 49980?

About 223.5621, exactly 14√255.

Is 49980 divisible by 3?

Yes. Its digits add up to 30, a multiple of 3.

What is special about the number 49980?

49980 is a Harshad number: divisible by its digit sum 30.