The number 12600

Q: Is 12600 a prime number?

No. 12600 = 2^3 × 3^2 × 5^2 × 7, so it is divisible by 2.

12600 is a composite number with 72 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × $5^{2}$ × 7. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21 … 12600.

Number

Pick any whole number from 1 to 100,000.

12600 = 2^{3} \times 3^{2} \times 5^{2} \times 7

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How to work it out

1
What is special about 12600: a Harshad number: divisible by its digit sum 9.
2
12600 is composite. Its prime factorisation is
$12600 = 2^{3} \times 3^{2} \times 5^{2} \times 7$
3
The divisors add up to 48360; without 12600 itself that is 35760, so 12600 is abundant (35760 is more than 12600). Euler's totient φ(12600) = 2880 numbers up to 12600 share no factor with it.
4
The digits of 12600 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 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 12600 = 2^{3} \times 3^{2} \times 5^{2} \times 7 \]

12600 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	48360
Euler totient φ(n)	2880
Square	158760000
Cube	2000376000000
Square root	112.249722 (= 30√14)
Digit sum / digital root	9 / 9
Collatz steps to 1	63
Scientific notation	1.26 × $10^{4}$

12600 in other forms

Form	Value
In words	twelve thousand six hundred
Binary (base 2)	11000100111000
Octal (base 8)	30470
Hexadecimal (base 16)	3138
Base 3	122021200
As time	12600 seconds = 3 h 30 min 0 s

Is 12600 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (12600 ÷ 2 = 6300)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (12600 ÷ 3 = 4200)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (12600 ÷ 4 = 3150)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (12600 ÷ 5 = 2520)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (12600 ÷ 6 = 2100)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (12600 ÷ 7 = 1800)	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	Yes (12600 ÷ 8 = 1575)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (12600 ÷ 9 = 1400)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (12600 ÷ 10 = 1260)	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 (12600 ÷ 12 = 1050)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 12600 a prime number?

No. 12600 = $2^{3}$ × $3^{2}$ × $5^{2}$ × 7, so it is divisible by 2.

What are the factors of 12600?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 50, 56, 60, 63, 70, 72, 75, 84, 90, 100, 105, 120, 126, 140, 150, 168, 175, 180, 200, 210, 225, 252, 280, 300, 315, 350, 360, 420, 450, 504, 525, 600, 630, 700, 840, 900, 1050, 1260, 1400, 1575, 1800, 2100, 2520, 3150, 4200, 6300, 12600.

What is 12600 in binary?

11000100111000 (hexadecimal 3138, octal 30470).

What is the square root of 12600?

About 112.2497, exactly 30√14.

Is 12600 divisible by 3?

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

What is special about the number 12600?

12600 is a Harshad number: divisible by its digit sum 9.