Math question: What is the sum of the multiples of 3, 5, and 8 between 20 and 240?

To find the sum of the multiples of a number within a range, we find the smallest multiple (20, in this case) and the largest multiple (240). First, we calculate the multiples of 3 by finding the smallest multiple greater than or equal to 20 (which is 21) and the largest multiple less than or equal to 240 (which is 240). Using the formula for the sum of an arithmetic sequence (S = n/2 * (a + l)), we have 3 + (3*2) + ... + 240. We apply this formula and find the sum of multiples = 82,560. Second, we calculate the multiples of 5 in the same manner, which gives us the sum of multiples = 10,428. Lastly, we calculate the multiples of 8, sum = 8,484. Now, we sum these three results together: 82,560 + 10,428 + 8,484 = 101,472. The sum of the multiples of 3, 5, and 8 between 20 and 240 is 101,472.

Math question: If I divide a number by 3, subtract 20, multiply by 5, and then add 100, the result is 240. What is the number?

Let's solve the equation step by step. Initially, we have an unknown number x. When divided by 3, we get x/3. Subtracting 20 gives us x/3 - 20. Multiplying by 5, we have 5(x/3 - 20). Adding 100, the equation becomes 5(x/3 - 20) + 100 = 240. Simplifying further, we obtain 5x/3 - 100 + 100 = 240. Combining like terms, we have 5x/3 = 240, which can be written as 5x = 720 after cross-multiplying. Finally, dividing both sides by 5, we find x = 720/5 = 144. Therefore, the number is 144.

Math question: What is the sum of all the prime numbers less than 240?

To find the sum of prime numbers less than 240, we need to list and sum all the primes. The primes less than 240 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, and 229. Adding them up, we get the sum as 3961. So, the sum of all prime numbers less than 240 is 3961.

Max	9223372036854775807
25835	Positive integer
0b10001100	Binary number
01771452	Octal number
0x129abf	Hex number
5.012 * 10^7	Scientific notation
2^4 * 5	Factorized form
*	Random number

240 (number)

240 is an even 3-digits composite number following 239 and preceding 241. In scientific notation, it is written as 2.40 × 10^2. The sum of its digits is 6. It has a total of 6 prime factors and 20 positive divisors. There are 64 positive integers (up to 240) that are relatively prime to 240.

Interesting facts

240 has 20 divisors, whose sum is 744
The reverse of 240 is 042
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 3
Sum of Digits 6
Digital Root 6

Name

Name	two hundred forty

Notation

Scientific notation	2.40 × 10^2
Engineering notation	2.40 × 10^0

Prime Factorization of 240

Prime Factorization 2 × 2 × 2 × 2 × 3 × 5

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	6	Total number of prime factors
rad	Radical	30	Product of the distinct prime numbers

The prime factorization of 240 is 2 × 2 × 2 × 2 × 3 × 5. Since it has a total of 6 prime factors.

Most popular turbo-numbers

9, 7, 99, 28, 927, 263, 9096, 7232, 67099, 56414, 389555, 201334, 3613869, 9745131, 16468693, 84793903, 151291458, 631824837, 1677952317, 3682090954

Basic calculations (n = 240)

Multiplication

n×y

n×2	480
n×3	720
n×4	960
n×5	1200

Division

n÷y

n÷2	120
n÷3	80
n÷3	60
n÷5	48

Exponentiation

n^y

n²	57600
n³	13824000
n⁴	3317760000
n⁵	796262400000

Nth Root

^y√n

²√n	15.49193338483
³√n	6.2144650119077
⁴√n	3.9359793425309
⁵√n	2.9925557394777

Divisors of 240

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

20 divisors

τ	Total Divisors	20	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-239	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.05	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	1	Returns the nth root of the product of n divisors
H	Harmonic Mean	20	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 240 can be divided by 20 positive divisors. The sum of these divisors (counting 240) is 1, the average is 0.05.

Base conversion 240

Base	System	Value
2	Binary	11110000
3	Ternary	22220
4	Quaternary	3300
5	Quinary	1430
6	Senary	1040
8	Octal	360
10	Decimal	240
12	Duodecimal	180
16	Hexadecimal	f0
20	Vigesimal	c0
36	Base36	6o

Cryptographic Hash Functions

md5	335f5352088d7d9bf74191e006d8e24c
sha1	cae91e45aed80f3a3fe285c3c8c1a7e78d82d473
sha256	6af1f692e9496c6d0b668316eccb93276ae6b6774fa728aac31ff40a38318760
sha512	15cad44ee4917cea357e1f11a5c3af098c9a11d71165a3f88942eef5669631fdedc733592a870c25f40ff5cca4a3566ee243229ebf42dcdd42d201da0050c51a
ripemd-160	4aab78ff99e92b90d41027e2d73c58899878996c

240 as geometric shapes

Circle

Radius = n

Diameter	480
Circumference	1507.9644737231
Area	180955.73684677

Sphere

Radius = n

Volume	57905835.790967
Surface area	723822.94738709
Circumference	1507.9644737231

Square

Length = n

Perimeter	960
Area	57600
Diagonal	339.41125496954

Cube

Length = n

Surface area	345600
Volume	13824000
Space diagonal	415.69219381653

Equilateral Triangle

Length = n

Perimeter	720
Area	24941.531628992
Altitude	207.84609690827

Triangular Pyramid

Length = n

Surface area	24941.531628992
Volume	1629174.0238538
Height	113.13708498985