The number 35700

Q: Is 35700 a prime number?

No. 35700 = 2^2 × 3 × 5^2 × 7 × 17, so it is divisible by 2.

35700 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × $5^{2}$ × 7 × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 25, 28 … 35700.

Number

Pick any whole number from 1 to 100,000.

35700 = 2^{2} \times 3 \times 5^{2} \times 7 \times 17

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How to work it out

1
What is special about 35700: a Harshad number: divisible by its digit sum 15.
2
35700 is composite. Its prime factorisation is
$35700 = 2^{2} \times 3 \times 5^{2} \times 7 \times 17$
3
The divisors add up to 124992; without 35700 itself that is 89292, so 35700 is abundant (89292 is more than 35700). Euler's totient φ(35700) = 7680 numbers up to 35700 share no factor with it.
4
The digits of 35700 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 98 steps to reach 1.

LaTeX source of the formulas on this page

\[ 35700 = 2^{2} \times 3 \times 5^{2} \times 7 \times 17 \]

35700 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	124992
Euler totient φ(n)	7680
Square	1274490000
Cube	45499293000000
Square root	188.944436 (= 10√357)
Digit sum / digital root	15 / 6
Collatz steps to 1	98
Scientific notation	3.57 × $10^{4}$

35700 in other forms

Form	Value
In words	thirty-five thousand seven hundred
Binary (base 2)	1000101101110100
Octal (base 8)	105564
Hexadecimal (base 16)	8B74
Base 3	1210222020
As time	35700 seconds = 9 h 55 min 0 s

Is 35700 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (35700 ÷ 2 = 17850)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (35700 ÷ 3 = 11900)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (35700 ÷ 4 = 8925)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (35700 ÷ 5 = 7140)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (35700 ÷ 6 = 5950)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (35700 ÷ 7 = 5100)	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 (35700 ÷ 10 = 3570)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 5)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (35700 ÷ 12 = 2975)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 35700 a prime number?

No. 35700 = $2^{2}$ × 3 × $5^{2}$ × 7 × 17, so it is divisible by 2.

What are the factors of 35700?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 25, 28, 30, 34, 35, 42, 50, 51, 60, 68, 70, 75, 84, 85, 100, 102, 105, 119, 140, 150, 170, 175, 204, 210, 238, 255, 300, 340, 350, 357, 420, 425, 476, 510, 525, 595, 700, 714, 850, 1020, 1050, 1190, 1275, 1428, 1700, 1785, 2100, 2380, 2550, 2975, 3570, 5100, 5950, 7140, 8925, 11900, 17850, 35700.

What is 35700 in binary?

1000101101110100 (hexadecimal 8B74, octal 105564).

What is the square root of 35700?

About 188.9444, exactly 10√357.

Is 35700 divisible by 3?

Yes. Its digits add up to 15, a multiple of 3.

What is special about the number 35700?

35700 is a Harshad number: divisible by its digit sum 15.