The number 97020

Q: Is 97020 a prime number?

No. 97020 = 2^2 × 3^2 × 5 × 7^2 × 11, so it is divisible by 2.

97020 is a triangular number: 1 + 2 + … + 440 = 97020. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × $7^{2}$ × 11. Divisors (108): 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21 … 97020.

Number

Pick any whole number from 1 to 100,000.

97020 = 2^{2} \times 3^{2} \times 5 \times 7^{2} \times 11

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How to work it out

1
What is special about 97020: a triangular number: 1 + 2 + … + 440 = 97020; a Harshad number: divisible by its digit sum 18.
2
97020 is composite. Its prime factorisation is
$97020 = 2^{2} \times 3^{2} \times 5 \times 7^{2} \times 11$
3
The divisors add up to 373464; without 97020 itself that is 276444, so 97020 is abundant (276444 is more than 97020). Euler's totient φ(97020) = 20160 numbers up to 97020 share no factor with it.
4
The digits of 97020 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 84 steps to reach 1.

LaTeX source of the formulas on this page

\[ 97020 = 2^{2} \times 3^{2} \times 5 \times 7^{2} \times 11 \]

97020 at a glance

Property	Value
Type	composite
Number of divisors	108
Sum of divisors	373464
Euler totient φ(n)	20160
Square	9412880400
Cube	913237656408000
Square root	311.480336 (= 42√55)
Digit sum / digital root	18 / 9
Collatz steps to 1	84
Scientific notation	9.702 × $10^{4}$

97020 in other forms

Form	Value
In words	ninety-seven thousand and twenty
Binary (base 2)	10111101011111100
Octal (base 8)	275374
Hexadecimal (base 16)	17AFC
Base 3	11221002100
As time	97020 seconds = 26 h 57 min 0 s

Is 97020 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (97020 ÷ 2 = 48510)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (97020 ÷ 3 = 32340)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (97020 ÷ 4 = 24255)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (97020 ÷ 5 = 19404)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (97020 ÷ 6 = 16170)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (97020 ÷ 7 = 13860)	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 (97020 ÷ 9 = 10780)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (97020 ÷ 10 = 9702)	A number is divisible by 10 if the last digit is 0.
11	Yes (97020 ÷ 11 = 8820)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (97020 ÷ 12 = 8085)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 97020 a prime number?

No. 97020 = $2^{2}$ × $3^{2}$ × 5 × $7^{2}$ × 11, so it is divisible by 2.

What are the factors of 97020?

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 28, 30, 33, 35, 36, 42, 44, 45, 49, 55, 60, 63, 66, 70, 77, 84, 90, 98, 99, 105, 110, 126, 132, 140, 147, 154, 165, 180, 196, 198, 210, 220, 231, 245, 252, 294, 308, 315, 330, 385, 396, 420, 441, 462, 490, 495, 539, 588, 630, 660, 693, 735, 770, 882, 924, 980, 990, 1078, 1155, 1260, 1386, 1470, 1540, 1617, 1764, 1980, 2156, 2205, 2310, 2695, 2772, 2940, 3234, 3465, 4410, 4620, 4851, 5390, 6468, 6930, 8085, 8820, 9702, 10780, 13860, 16170, 19404, 24255, 32340, 48510, 97020.

What is 97020 in binary?

10111101011111100 (hexadecimal 17AFC, octal 275374).

What is the square root of 97020?

About 311.4803, exactly 42√55.

Is 97020 divisible by 3?

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

What is special about the number 97020?

97020 is a triangular number: 1 + 2 + … + 440 = 97020; a Harshad number: divisible by its digit sum 18.