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The number 37984

37984 is a composite number with 12 divisors. Its prime factorisation is 252^{5} × 1187. Divisors (12): 1, 2, 4, 8, 16, 32, 1187, 2374, 4748, 9496, 18992, 37984.

Number

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How to work it out

  1. 1

    What is special about 37984: a happy number: repeatedly adding the squares of its digits reaches 1.

  2. 2

    37984 is composite. Its prime factorisation is

    37984=25×118737984 = 2^{5} \times 1187
  3. 3

    The divisors add up to 74844; without 37984 itself that is 36860, so 37984 is deficient (36860 is less than 37984). Euler's totient φ(37984) = 18976 numbers up to 37984 share no factor with it.

  4. 4

    The digits of 37984 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.

LaTeX source of the formulas on this page
\[ 37984 = 2^{5} \times 1187 \]

37984 at a glance

PropertyValue
Typecomposite
Number of divisors12
Sum of divisors74844
Euler totient φ(n)18976
Square1442784256
Cube54802717179904
Square root194.894843 (= 4√2374)
Digit sum / digital root31 / 4
Collatz steps to 180
Scientific notation3.7984 × 10410^{4}

37984 in other forms

FormValue
In wordsthirty-seven thousand nine hundred and eighty-four
Binary (base 2)1001010001100000
Octal (base 8)112140
Hexadecimal (base 16)9460
Base 31221002211
As time37984 seconds = 10 h 33 min 4 s

Is 37984 divisible by 2 to 12?

DivisorAnswerRule
2Yes (37984 ÷ 2 = 18992)A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3No (remainder 1)A number is divisible by 3 if the digits add up to a multiple of 3.
4Yes (37984 ÷ 4 = 9496)A number is divisible by 4 if the last two digits make a multiple of 4.
5No (remainder 4)A number is divisible by 5 if the last digit is 0 or 5.
6No (remainder 4)A number is divisible by 6 if it is divisible by both 2 and 3.
7No (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.
8Yes (37984 ÷ 8 = 4748)A number is divisible by 8 if the last three digits make a multiple of 8.
9No (remainder 4)A number is divisible by 9 if the digits add up to a multiple of 9.
10No (remainder 4)A number is divisible by 10 if the last digit is 0.
11No (remainder 1)A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12No (remainder 4)A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 37984 a prime number?

No. 37984 = 252^{5} × 1187, so it is divisible by 2.

What are the factors of 37984?

1, 2, 4, 8, 16, 32, 1187, 2374, 4748, 9496, 18992, 37984.

What is 37984 in binary?

1001010001100000 (hexadecimal 9460, octal 112140).

What is the square root of 37984?

About 194.8948, exactly 4√2374.

Is 37984 divisible by 3?

No. Its digits add up to 31, which is not a multiple of 3.

What is special about the number 37984?

37984 is a happy number: repeatedly adding the squares of its digits reaches 1.

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    37984: is it prime? Factors, square root, binary, Roman numeral | WordGPT