The number 97980

Q: Is 97980 a prime number?

No. 97980 = 2^2 × 3 × 5 × 23 × 71, so it is divisible by 2.

97980 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × 23 × 71. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 71 … 97980.

Number

Pick any whole number from 1 to 100,000.

97980 = 2^{2} \times 3 \times 5 \times 23 \times 71

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How to work it out

1
97980 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
97980 is composite. Its prime factorisation is
$97980 = 2^{2} \times 3 \times 5 \times 23 \times 71$
3
The divisors add up to 290304; without 97980 itself that is 192324, so 97980 is abundant (192324 is more than 97980). Euler's totient φ(97980) = 24640 numbers up to 97980 share no factor with it.
4
The digits of 97980 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 66 steps to reach 1.

LaTeX source of the formulas on this page

\[ 97980 = 2^{2} \times 3 \times 5 \times 23 \times 71 \]

97980 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	290304
Euler totient φ(n)	24640
Square	9600080400
Cube	940615877592000
Square root	313.017571 (= 2√24495)
Digit sum / digital root	33 / 6
Collatz steps to 1	66
Scientific notation	9.798 × $10^{4}$

97980 in other forms

Form	Value
In words	ninety-seven thousand nine hundred and eighty
Binary (base 2)	10111111010111100
Octal (base 8)	277274
Hexadecimal (base 16)	17EBC
Base 3	11222101220
As time	97980 seconds = 27 h 13 min 0 s

Is 97980 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (97980 ÷ 2 = 48990)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (97980 ÷ 3 = 32660)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (97980 ÷ 4 = 24495)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (97980 ÷ 5 = 19596)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (97980 ÷ 6 = 16330)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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 6)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (97980 ÷ 10 = 9798)	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 (97980 ÷ 12 = 8165)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 97980 a prime number?

No. 97980 = $2^{2}$ × 3 × 5 × 23 × 71, so it is divisible by 2.

What are the factors of 97980?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 71, 92, 115, 138, 142, 213, 230, 276, 284, 345, 355, 426, 460, 690, 710, 852, 1065, 1380, 1420, 1633, 2130, 3266, 4260, 4899, 6532, 8165, 9798, 16330, 19596, 24495, 32660, 48990, 97980.

What is 97980 in binary?

10111111010111100 (hexadecimal 17EBC, octal 277274).

What is the square root of 97980?

About 313.0176, exactly 2√24495.

Is 97980 divisible by 3?

Yes. Its digits add up to 33, a multiple of 3.

What is special about the number 97980?

It is a composite number with 48 divisors.