The number 35100

Q: Is 35100 a prime number?

No. 35100 = 2^2 × 3^3 × 5^2 × 13, so it is divisible by 2.

35100 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{3}$ × $5^{2}$ × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 25, 26, 27 … 35100.

Number

Pick any whole number from 1 to 100,000.

35100 = 2^{2} \times 3^{3} \times 5^{2} \times 13

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How to work it out

1
What is special about 35100: a Harshad number: divisible by its digit sum 9.
2
35100 is composite. Its prime factorisation is
$35100 = 2^{2} \times 3^{3} \times 5^{2} \times 13$
3
The divisors add up to 121520; without 35100 itself that is 86420, so 35100 is abundant (86420 is more than 35100). Euler's totient φ(35100) = 8640 numbers up to 35100 share no factor with it.
4
The digits of 35100 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 142 steps to reach 1.

LaTeX source of the formulas on this page

\[ 35100 = 2^{2} \times 3^{3} \times 5^{2} \times 13 \]

35100 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	121520
Euler totient φ(n)	8640
Square	1232010000
Cube	43243551000000
Square root	187.349940 (= 30√39)
Digit sum / digital root	9 / 9
Collatz steps to 1	142
Scientific notation	3.51 × $10^{4}$

35100 in other forms

Form	Value
In words	thirty-five thousand one hundred
Binary (base 2)	1000100100011100
Octal (base 8)	104434
Hexadecimal (base 16)	891C
Base 3	1210011000
As time	35100 seconds = 9 h 45 min 0 s

Is 35100 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (35100 ÷ 2 = 17550)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (35100 ÷ 3 = 11700)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (35100 ÷ 4 = 8775)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (35100 ÷ 5 = 7020)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (35100 ÷ 6 = 5850)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	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 (35100 ÷ 9 = 3900)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (35100 ÷ 10 = 3510)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (35100 ÷ 12 = 2925)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 35100 a prime number?

No. 35100 = $2^{2}$ × $3^{3}$ × $5^{2}$ × 13, so it is divisible by 2.

What are the factors of 35100?

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 25, 26, 27, 30, 36, 39, 45, 50, 52, 54, 60, 65, 75, 78, 90, 100, 108, 117, 130, 135, 150, 156, 180, 195, 225, 234, 260, 270, 300, 325, 351, 390, 450, 468, 540, 585, 650, 675, 702, 780, 900, 975, 1170, 1300, 1350, 1404, 1755, 1950, 2340, 2700, 2925, 3510, 3900, 5850, 7020, 8775, 11700, 17550, 35100.

What is 35100 in binary?

1000100100011100 (hexadecimal 891C, octal 104434).

What is the square root of 35100?

About 187.3499, exactly 30√39.

Is 35100 divisible by 3?

Yes. Its digits add up to 9, a multiple of 3.

What is special about the number 35100?

35100 is a Harshad number: divisible by its digit sum 9.