The number 48972

Q: Is 48972 a prime number?

No. 48972 = 2^2 × 3 × 7 × 11 × 53, so it is divisible by 2.

48972 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 7 × 11 × 53. Divisors (48): 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 53 … 48972.

Number

Pick any whole number from 1 to 100,000.

48972 = 2^{2} \times 3 \times 7 \times 11 \times 53

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How to work it out

1
48972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
48972 is composite. Its prime factorisation is
$48972 = 2^{2} \times 3 \times 7 \times 11 \times 53$
3
The divisors add up to 145152; without 48972 itself that is 96180, so 48972 is abundant (96180 is more than 48972). Euler's totient φ(48972) = 12480 numbers up to 48972 share no factor with it.
4
The digits of 48972 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 176 steps to reach 1.

LaTeX source of the formulas on this page

\[ 48972 = 2^{2} \times 3 \times 7 \times 11 \times 53 \]

48972 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	145152
Euler totient φ(n)	12480
Square	2398256784
Cube	117447431226048
Square root	221.296182 (= 2√12243)
Digit sum / digital root	30 / 3
Collatz steps to 1	176
Scientific notation	4.8972 × $10^{4}$

48972 in other forms

Form	Value
In words	forty-eight thousand nine hundred and seventy-two
Binary (base 2)	1011111101001100
Octal (base 8)	137514
Hexadecimal (base 16)	BF4C
Base 3	2111011210
As time	48972 seconds = 13 h 36 min 12 s

Is 48972 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (48972 ÷ 2 = 24486)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (48972 ÷ 3 = 16324)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (48972 ÷ 4 = 12243)	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 (48972 ÷ 6 = 8162)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (48972 ÷ 7 = 6996)	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	No (remainder 2)	A number is divisible by 10 if the last digit is 0.
11	Yes (48972 ÷ 11 = 4452)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (48972 ÷ 12 = 4081)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 48972 a prime number?

No. 48972 = $2^{2}$ × 3 × 7 × 11 × 53, so it is divisible by 2.

What are the factors of 48972?

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 53, 66, 77, 84, 106, 132, 154, 159, 212, 231, 308, 318, 371, 462, 583, 636, 742, 924, 1113, 1166, 1484, 1749, 2226, 2332, 3498, 4081, 4452, 6996, 8162, 12243, 16324, 24486, 48972.

What is 48972 in binary?

1011111101001100 (hexadecimal BF4C, octal 137514).

What is the square root of 48972?

About 221.2962, exactly 2√12243.

Is 48972 divisible by 3?

Yes. Its digits add up to 30, a multiple of 3.

What is special about the number 48972?

It is a composite number with 48 divisors.