The number 75140

Q: Is 75140 a prime number?

No. 75140 = 2^2 × 5 × 13 × 17^2, so it is divisible by 2.

75140 is a composite number with 36 divisors. Its prime factorisation is $2^{2}$ × 5 × 13 × $17^{2}$ . Divisors (36): 1, 2, 4, 5, 10, 13, 17, 20, 26, 34, 52, 65, 68, 85, 130, 170 … 75140.

Number

Pick any whole number from 1 to 100,000.

75140 = 2^{2} \times 5 \times 13 \times 17^{2}

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How to work it out

1
What is special about 75140: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 17.
2
75140 is composite. Its prime factorisation is
$75140 = 2^{2} \times 5 \times 13 \times 17^{2}$
3
The divisors add up to 180516; without 75140 itself that is 105376, so 75140 is abundant (105376 is more than 75140). Euler's totient φ(75140) = 26112 numbers up to 75140 share no factor with it.
4
The digits of 75140 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 68 steps to reach 1.

LaTeX source of the formulas on this page

\[ 75140 = 2^{2} \times 5 \times 13 \times 17^{2} \]

75140 at a glance

Property	Value
Type	composite
Number of divisors	36
Sum of divisors	180516
Euler totient φ(n)	26112
Square	5646019600
Cube	424241912744000
Square root	274.116763 (= 34√65)
Digit sum / digital root	17 / 8
Collatz steps to 1	68
Scientific notation	7.514 × $10^{4}$

75140 in other forms

Form	Value
In words	seventy-five thousand one hundred and forty
Binary (base 2)	10010010110000100
Octal (base 8)	222604
Hexadecimal (base 16)	12584
Base 3	10211001222
As time	75140 seconds = 20 h 52 min 20 s

Is 75140 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (75140 ÷ 2 = 37570)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	No (remainder 2)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (75140 ÷ 4 = 18785)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (75140 ÷ 5 = 15028)	A number is divisible by 5 if the last digit is 0 or 5.
6	No (remainder 2)	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	No (remainder 8)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (75140 ÷ 10 = 7514)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 10)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	No (remainder 8)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 75140 a prime number?

No. 75140 = $2^{2}$ × 5 × 13 × $17^{2}$ , so it is divisible by 2.

What are the factors of 75140?

1, 2, 4, 5, 10, 13, 17, 20, 26, 34, 52, 65, 68, 85, 130, 170, 221, 260, 289, 340, 442, 578, 884, 1105, 1156, 1445, 2210, 2890, 3757, 4420, 5780, 7514, 15028, 18785, 37570, 75140.

What is 75140 in binary?

10010010110000100 (hexadecimal 12584, octal 222604).

What is the square root of 75140?

About 274.1168, exactly 34√65.

Is 75140 divisible by 3?

No. Its digits add up to 17, which is not a multiple of 3.

What is special about the number 75140?

75140 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 17.