The number 61740

Q: Is 61740 a prime number?

No. 61740 = 2^2 × 3^2 × 5 × 7^3, so it is divisible by 2.

61740 is a composite number with 72 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 5 × $7^{3}$ . Divisors (72): 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28 … 61740.

Number

Pick any whole number from 1 to 100,000.

61740 = 2^{2} \times 3^{2} \times 5 \times 7^{3}

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How to work it out

1
What is special about 61740: a Harshad number: divisible by its digit sum 18.
2
61740 is composite. Its prime factorisation is
$61740 = 2^{2} \times 3^{2} \times 5 \times 7^{3}$
3
The divisors add up to 218400; without 61740 itself that is 156660, so 61740 is abundant (156660 is more than 61740). Euler's totient φ(61740) = 14112 numbers up to 61740 share no factor with it.
4
The digits of 61740 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 55 steps to reach 1.

LaTeX source of the formulas on this page

\[ 61740 = 2^{2} \times 3^{2} \times 5 \times 7^{3} \]

61740 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	218400
Euler totient φ(n)	14112
Square	3811827600
Cube	235342236024000
Square root	248.475351 (= 42√35)
Digit sum / digital root	18 / 9
Collatz steps to 1	55
Scientific notation	6.174 × $10^{4}$

61740 in other forms

Form	Value
In words	sixty-one thousand seven hundred and forty
Binary (base 2)	1111000100101100
Octal (base 8)	170454
Hexadecimal (base 16)	F12C
Base 3	10010200200
As time	61740 seconds = 17 h 9 min 0 s

Is 61740 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (61740 ÷ 2 = 30870)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (61740 ÷ 3 = 20580)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (61740 ÷ 4 = 15435)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (61740 ÷ 5 = 12348)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (61740 ÷ 6 = 10290)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (61740 ÷ 7 = 8820)	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 (61740 ÷ 9 = 6860)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (61740 ÷ 10 = 6174)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (61740 ÷ 12 = 5145)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 61740 a prime number?

No. 61740 = $2^{2}$ × $3^{2}$ × 5 × $7^{3}$ , so it is divisible by 2.

What are the factors of 61740?

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 49, 60, 63, 70, 84, 90, 98, 105, 126, 140, 147, 180, 196, 210, 245, 252, 294, 315, 343, 420, 441, 490, 588, 630, 686, 735, 882, 980, 1029, 1260, 1372, 1470, 1715, 1764, 2058, 2205, 2940, 3087, 3430, 4116, 4410, 5145, 6174, 6860, 8820, 10290, 12348, 15435, 20580, 30870, 61740.

What is 61740 in binary?

1111000100101100 (hexadecimal F12C, octal 170454).

What is the square root of 61740?

About 248.4754, exactly 42√35.

Is 61740 divisible by 3?

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

What is special about the number 61740?

61740 is a Harshad number: divisible by its digit sum 18.