The number 77532

Q: Is 77532 a prime number?

No. 77532 = 2^2 × 3 × 7 × 13 × 71, so it is divisible by 2.

77532 is a composite number with 48 divisors. Its prime factorisation is $2^{2}$ × 3 × 7 × 13 × 71. Divisors (48): 1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 71 … 77532.

Number

Pick any whole number from 1 to 100,000.

77532 = 2^{2} \times 3 \times 7 \times 13 \times 71

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How to work it out

1
77532 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
77532 is composite. Its prime factorisation is
$77532 = 2^{2} \times 3 \times 7 \times 13 \times 71$
3
The divisors add up to 225792; without 77532 itself that is 148260, so 77532 is abundant (148260 is more than 77532). Euler's totient φ(77532) = 20160 numbers up to 77532 share no factor with it.
4
The digits of 77532 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 63 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77532 = 2^{2} \times 3 \times 7 \times 13 \times 71 \]

77532 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	225792
Euler totient φ(n)	20160
Square	6011211024
Cube	466061213112768
Square root	278.445686 (= 2√19383)
Digit sum / digital root	24 / 6
Collatz steps to 1	63
Scientific notation	7.7532 × $10^{4}$

77532 in other forms

Form	Value
In words	seventy-seven thousand five hundred and thirty-two
Binary (base 2)	10010111011011100
Octal (base 8)	227334
Hexadecimal (base 16)	12EDC
Base 3	10221100120
As time	77532 seconds = 21 h 32 min 12 s

Is 77532 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77532 ÷ 2 = 38766)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77532 ÷ 3 = 25844)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77532 ÷ 4 = 19383)	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 (77532 ÷ 6 = 12922)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	Yes (77532 ÷ 7 = 11076)	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 6)	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 4)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (77532 ÷ 12 = 6461)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77532 a prime number?

No. 77532 = $2^{2}$ × 3 × 7 × 13 × 71, so it is divisible by 2.

What are the factors of 77532?

1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 71, 78, 84, 91, 142, 156, 182, 213, 273, 284, 364, 426, 497, 546, 852, 923, 994, 1092, 1491, 1846, 1988, 2769, 2982, 3692, 5538, 5964, 6461, 11076, 12922, 19383, 25844, 38766, 77532.

What is 77532 in binary?

10010111011011100 (hexadecimal 12EDC, octal 227334).

What is the square root of 77532?

About 278.4457, exactly 2√19383.

Is 77532 divisible by 3?

Yes. Its digits add up to 24, a multiple of 3.

What is special about the number 77532?

It is a composite number with 48 divisors.