The number 77400

Q: Is 77400 a prime number?

No. 77400 = 2^3 × 3^2 × 5^2 × 43, so it is divisible by 2.

77400 is a composite number with 72 divisors. Its prime factorisation is $2^{3}$ × $3^{2}$ × $5^{2}$ × 43. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30 … 77400.

Number

Pick any whole number from 1 to 100,000.

77400 = 2^{3} \times 3^{2} \times 5^{2} \times 43

Explain it step by step in chat Make a short video of it

How to work it out

1
What is special about 77400: a Harshad number: divisible by its digit sum 18.
2
77400 is composite. Its prime factorisation is
$77400 = 2^{3} \times 3^{2} \times 5^{2} \times 43$
3
The divisors add up to 265980; without 77400 itself that is 188580, so 77400 is abundant (188580 is more than 77400). Euler's totient φ(77400) = 20160 numbers up to 77400 share no factor with it.
4
The digits of 77400 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.

LaTeX source of the formulas on this page

\[ 77400 = 2^{3} \times 3^{2} \times 5^{2} \times 43 \]

77400 at a glance

Property	Value
Type	composite
Number of divisors	72
Sum of divisors	265980
Euler totient φ(n)	20160
Square	5990760000
Cube	463684824000000
Square root	278.208555 (= 30√86)
Digit sum / digital root	18 / 9
Collatz steps to 1	76
Scientific notation	7.74 × $10^{4}$

77400 in other forms

Form	Value
In words	seventy-seven thousand four hundred
Binary (base 2)	10010111001011000
Octal (base 8)	227130
Hexadecimal (base 16)	12E58
Base 3	10221011200
As time	77400 seconds = 21 h 30 min 0 s

Is 77400 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (77400 ÷ 2 = 38700)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (77400 ÷ 3 = 25800)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (77400 ÷ 4 = 19350)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (77400 ÷ 5 = 15480)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (77400 ÷ 6 = 12900)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 1)	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	Yes (77400 ÷ 8 = 9675)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	Yes (77400 ÷ 9 = 8600)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (77400 ÷ 10 = 7740)	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 (77400 ÷ 12 = 6450)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 77400 a prime number?

No. 77400 = $2^{3}$ × $3^{2}$ × $5^{2}$ × 43, so it is divisible by 2.

What are the factors of 77400?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 43, 45, 50, 60, 72, 75, 86, 90, 100, 120, 129, 150, 172, 180, 200, 215, 225, 258, 300, 344, 360, 387, 430, 450, 516, 600, 645, 774, 860, 900, 1032, 1075, 1290, 1548, 1720, 1800, 1935, 2150, 2580, 3096, 3225, 3870, 4300, 5160, 6450, 7740, 8600, 9675, 12900, 15480, 19350, 25800, 38700, 77400.

What is 77400 in binary?

10010111001011000 (hexadecimal 12E58, octal 227130).

What is the square root of 77400?

About 278.2086, exactly 30√86.

Is 77400 divisible by 3?

Yes. Its digits add up to 18, a multiple of 3.

What is special about the number 77400?

77400 is a Harshad number: divisible by its digit sum 18.