The number 67620

Q: Is 67620 a prime number?

No. 67620 = 2^2 × 3 × 5 × 7^2 × 23, so it is divisible by 2.

67620 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × 3 × 5 × $7^{2}$ × 23. Divisors (72): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 28, 30 … 67620.

Number

Pick any whole number from 1 to 100,000.

67620 = 2^{2} \times 3 \times 5 \times 7^{2} \times 23

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 67620: a Harshad number: divisible by its digit sum 21.
2
67620 is composite. Its prime factorisation is
$67620 = 2^{2} \times 3 \times 5 \times 7^{2} \times 23$
3
The divisors add up to 229824; without 67620 itself that is 162204, so 67620 is abundant (162204 is more than 67620). Euler's totient φ(67620) = 14784 numbers up to 67620 share no factor with it.
4
The digits of 67620 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 60 steps to reach 1.

LaTeX source of the formulas on this page

\[ 67620 = 2^{2} \times 3 \times 5 \times 7^{2} \times 23 \]

67620 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	229824
Euler totient φ(n)	14784
Square	4572464400
Cube	309190042728000
Square root	260.038459 (= 14√345)
Digit sum / digital root	21 / 3
Collatz steps to 1	60
Scientific notation	6.762 × $10^{4}$

67620 in other forms

Form	Value
In words	sixty-seven thousand six hundred and twenty
Binary (base 2)	10000100000100100
Octal (base 8)	204044
Hexadecimal (base 16)	10824
Base 3	10102202110
As time	67620 seconds = 18 h 47 min 0 s

Is 67620 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (67620 ÷ 2 = 33810)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (67620 ÷ 3 = 22540)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (67620 ÷ 4 = 16905)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (67620 ÷ 5 = 13524)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (67620 ÷ 6 = 11270)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (67620 ÷ 7 = 9660)	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 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (67620 ÷ 10 = 6762)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 3)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (67620 ÷ 12 = 5635)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 67620 a prime number?

No. 67620 = $2^{2}$ × 3 × 5 × $7^{2}$ × 23, so it is divisible by 2.

What are the factors of 67620?

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 28, 30, 35, 42, 46, 49, 60, 69, 70, 84, 92, 98, 105, 115, 138, 140, 147, 161, 196, 210, 230, 245, 276, 294, 322, 345, 420, 460, 483, 490, 588, 644, 690, 735, 805, 966, 980, 1127, 1380, 1470, 1610, 1932, 2254, 2415, 2940, 3220, 3381, 4508, 4830, 5635, 6762, 9660, 11270, 13524, 16905, 22540, 33810, 67620.

What is 67620 in binary?

10000100000100100 (hexadecimal 10824, octal 204044).

What is the square root of 67620?

About 260.0385, exactly 14√345.

Is 67620 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 67620?

67620 is a Harshad number: divisible by its digit sum 21.