The number 90972

Q: Is 90972 a prime number?

No. 90972 = 2^2 × 3^2 × 7 × 19^2, so it is divisible by 2.

90972 is a composite number with 54 divisors. Its prime factorisation is $2^{2}$ × $3^{2}$ × 7 × $19^{2}$ . Divisors (54): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 19, 21, 28, 36, 38, 42 … 90972.

Number

Pick any whole number from 1 to 100,000.

90972 = 2^{2} \times 3^{2} \times 7 \times 19^{2}

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How to work it out

1
90972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
90972 is composite. Its prime factorisation is
$90972 = 2^{2} \times 3^{2} \times 7 \times 19^{2}$
3
The divisors add up to 277368; without 90972 itself that is 186396, so 90972 is abundant (186396 is more than 90972). Euler's totient φ(90972) = 24624 numbers up to 90972 share no factor with it.
4
The digits of 90972 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 84 steps to reach 1.

LaTeX source of the formulas on this page

\[ 90972 = 2^{2} \times 3^{2} \times 7 \times 19^{2} \]

90972 at a glance

Property	Value
Type	composite
Number of divisors	54
Sum of divisors	277368
Euler totient φ(n)	24624
Square	8275904784
Cube	752875610010048
Square root	301.615649 (= 114√7)
Digit sum / digital root	27 / 9
Collatz steps to 1	84
Scientific notation	9.0972 × $10^{4}$

90972 in other forms

Form	Value
In words	ninety thousand nine hundred and seventy-two
Binary (base 2)	10110001101011100
Octal (base 8)	261534
Hexadecimal (base 16)	1635C
Base 3	11121210100
As time	90972 seconds = 25 h 16 min 12 s

Is 90972 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (90972 ÷ 2 = 45486)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (90972 ÷ 3 = 30324)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (90972 ÷ 4 = 22743)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 2)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (90972 ÷ 6 = 15162)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (90972 ÷ 7 = 12996)	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 (90972 ÷ 9 = 10108)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	No (remainder 2)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 2)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (90972 ÷ 12 = 7581)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 90972 a prime number?

No. 90972 = $2^{2}$ × $3^{2}$ × 7 × $19^{2}$ , so it is divisible by 2.

What are the factors of 90972?

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 19, 21, 28, 36, 38, 42, 57, 63, 76, 84, 114, 126, 133, 171, 228, 252, 266, 342, 361, 399, 532, 684, 722, 798, 1083, 1197, 1444, 1596, 2166, 2394, 2527, 3249, 4332, 4788, 5054, 6498, 7581, 10108, 12996, 15162, 22743, 30324, 45486, 90972.

What is 90972 in binary?

10110001101011100 (hexadecimal 1635C, octal 261534).

What is the square root of 90972?

About 301.6156, exactly 114√7.

Is 90972 divisible by 3?

Yes. Its digits add up to 27, a multiple of 3.

What is special about the number 90972?

It is a composite number with 54 divisors.