The number 37620

Q: Is 37620 a prime number?

No. 37620 = 2^2 × 3^2 × 5 × 11 × 19, so it is divisible by 2.

37620 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × 11 × 19. Divisors (72): 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 19, 20, 22, 30 … 37620.

Number

Pick any whole number from 1 to 100,000.

37620 = 2^{2} \times 3^{2} \times 5 \times 11 \times 19

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How to work it out

1
What is special about 37620: a Harshad number: divisible by its digit sum 18.
2
37620 is composite. Its prime factorisation is
$37620 = 2^{2} \times 3^{2} \times 5 \times 11 \times 19$
3
The divisors add up to 131040; without 37620 itself that is 93420, so 37620 is abundant (93420 is more than 37620). Euler's totient φ(37620) = 8640 numbers up to 37620 share no factor with it.
4
The digits of 37620 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 62 steps to reach 1.

LaTeX source of the formulas on this page

\[ 37620 = 2^{2} \times 3^{2} \times 5 \times 11 \times 19 \]

37620 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	131040
Euler totient φ(n)	8640
Square	1415264400
Cube	53242246728000
Square root	193.958759 (= 6√1045)
Digit sum / digital root	18 / 9
Collatz steps to 1	62
Scientific notation	3.762 × $10^{4}$

37620 in other forms

Form	Value
In words	thirty-seven thousand six hundred and twenty
Binary (base 2)	1001001011110100
Octal (base 8)	111364
Hexadecimal (base 16)	92F4
Base 3	1220121100
As time	37620 seconds = 10 h 27 min 0 s

Is 37620 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (37620 ÷ 2 = 18810)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (37620 ÷ 3 = 12540)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (37620 ÷ 4 = 9405)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (37620 ÷ 5 = 7524)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (37620 ÷ 6 = 6270)	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 (37620 ÷ 9 = 4180)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (37620 ÷ 10 = 3762)	A number is divisible by 10 if the last digit is 0.
11	Yes (37620 ÷ 11 = 3420)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (37620 ÷ 12 = 3135)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 37620 a prime number?

No. 37620 = $2^{2}$ × $3^{2}$ × 5 × 11 × 19, so it is divisible by 2.

What are the factors of 37620?

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 19, 20, 22, 30, 33, 36, 38, 44, 45, 55, 57, 60, 66, 76, 90, 95, 99, 110, 114, 132, 165, 171, 180, 190, 198, 209, 220, 228, 285, 330, 342, 380, 396, 418, 495, 570, 627, 660, 684, 836, 855, 990, 1045, 1140, 1254, 1710, 1881, 1980, 2090, 2508, 3135, 3420, 3762, 4180, 6270, 7524, 9405, 12540, 18810, 37620.

What is 37620 in binary?

1001001011110100 (hexadecimal 92F4, octal 111364).

What is the square root of 37620?

About 193.9588, exactly 6√1045.

Is 37620 divisible by 3?

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

What is special about the number 37620?

37620 is a Harshad number: divisible by its digit sum 18.