The number 20748

Q: Is 20748 a prime number?

No. 20748 = 2^2 × 3 × 7 × 13 × 19, so it is divisible by 2.

20748 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 7 × 13 × 19. Divisors (48): 1, 2, 3, 4, 6, 7, 12, 13, 14, 19, 21, 26, 28, 38, 39, 42 … 20748.

Number

Pick any whole number from 1 to 100,000.

20748 = 2^{2} \times 3 \times 7 \times 13 \times 19

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How to work it out

1
What is special about 20748: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
2
20748 is composite. Its prime factorisation is
$20748 = 2^{2} \times 3 \times 7 \times 13 \times 19$
3
The divisors add up to 62720; without 20748 itself that is 41972, so 20748 is abundant (41972 is more than 20748). Euler's totient φ(20748) = 5184 numbers up to 20748 share no factor with it.
4
The digits of 20748 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 43 steps to reach 1.

LaTeX source of the formulas on this page

\[ 20748 = 2^{2} \times 3 \times 7 \times 13 \times 19 \]

20748 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	62720
Euler totient φ(n)	5184
Square	430479504
Cube	8931588748992
Square root	144.041661 (= 2√5187)
Digit sum / digital root	21 / 3
Collatz steps to 1	43
Scientific notation	2.0748 × $10^{4}$

20748 in other forms

Form	Value
In words	twenty thousand seven hundred and forty-eight
Binary (base 2)	101000100001100
Octal (base 8)	50414
Hexadecimal (base 16)	510C
Base 3	1001110110
As time	20748 seconds = 5 h 45 min 48 s

Is 20748 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (20748 ÷ 2 = 10374)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (20748 ÷ 3 = 6916)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (20748 ÷ 4 = 5187)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	No (remainder 3)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (20748 ÷ 6 = 3458)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (20748 ÷ 7 = 2964)	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 8)	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 (20748 ÷ 12 = 1729)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 20748 a prime number?

No. 20748 = $2^{2}$ × 3 × 7 × 13 × 19, so it is divisible by 2.

What are the factors of 20748?

1, 2, 3, 4, 6, 7, 12, 13, 14, 19, 21, 26, 28, 38, 39, 42, 52, 57, 76, 78, 84, 91, 114, 133, 156, 182, 228, 247, 266, 273, 364, 399, 494, 532, 546, 741, 798, 988, 1092, 1482, 1596, 1729, 2964, 3458, 5187, 6916, 10374, 20748.

What is 20748 in binary?

101000100001100 (hexadecimal 510C, octal 50414).

What is the square root of 20748?

About 144.0417, exactly 2√5187.

Is 20748 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 20748?

20748 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.