What is the smallest positive integer n such that 840 is divisible by x, y, z, and n, where x, y, and z are three different prime numbers?

To find the smallest positive integer n, we need to factorize 840. The prime factorization of 840 is 2^3 × 3 × 5 × 7. Since x, y, and z are three different primes, they can be any combination of 2, 3, 5, and 7. To ensure 840 is divisible by x, y, and z, we need to find the prime number missing from the factorization. In this case, the missing prime is 7. Thus, n has to be 7 for 840 to be divisible by x, y, z, and n.

Math question: What is the least common multiple (LCM) of 840 and 5?

To find the LCM of 840 and 5, we need to determine the smallest multiple that is divisible by both numbers. First, let's prime factorize 840. Starting with the smallest prime, 2, we find that 840 = 2^3 × 3 × 5 × 7. Now, extending this prime factorization, let's determine the multiples of 5: 5, 10, 15, 20, ... We see that the smallest multiple shared by both 840 and 5 is the first multiple of 5 greater than 840, which is 845. Therefore, the LCM of 840 and 5 is 845. It is the smallest positive integer that is divisible by both 840 and 5.

Question: If I divide a number by 7, multiply the result by 12, and add the product to 48, the final value is 840. What is the original number?

Let's assume the original number is 'x'. According to the given condition, (x/7) * 12 + 48 = 840. Simplifying this equation, we have (12x/7) + 48 = 840. Rearranging it, we get 12x/7 = 840 - 48. Then, 12x/7 = 792. Cross-multiplying, we have 12x = 7 * 792. Solving for 'x', we find x = (7 * 792) / 12 = 396. Therefore, the original number is 396.

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

840 (number)

840 is an even 3-digits composite number following 839 and preceding 841. In scientific notation, it is written as 8.40 × 10^2. The sum of its digits is 12. It has a total of 5 prime factors and 16 positive divisors. There are 192 positive integers (up to 840) that are relatively prime to 840.

Interesting facts

840 has 16 divisors, whose sum is 1920
The reverse of 840 is 048
Previous prime number is 15

Basic properties

Is Prime? no
Number parity even
Number length 3
Sum of Digits 12
Digital Root 3

Name

Name	eight hundred forty

Notation

Scientific notation	8.40 × 10^2
Engineering notation	8.40 × 10^0

Prime Factorization of 840

Prime Factorization 2 × 2 × 2 × 15 × 7

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	5	Total number of prime factors
rad	Radical	210	Product of the distinct prime numbers

The prime factorization of 840 is 2 × 2 × 2 × 15 × 7. Since it has a total of 5 prime factors.

Most popular turbo-numbers

3, 4, 26, 74, 290, 101, 4297, 8086, 92384, 96245, 39774, 784158, 9510087, 2018932, 95381690, 47937337, 447545589, 641085310, 8262585753, 9221808109

Basic calculations (n = 840)

Multiplication

n×y

n×2	1680
n×3	2520
n×4	3360
n×5	4200

Division

n÷y

n÷2	420
n÷3	280
n÷3	210
n÷5	168

Exponentiation

n^y

n²	705600
n³	592704000
n⁴	497871360000
n⁵	418211942400000

Nth Root

^y√n

²√n	28.982753492379
³√n	9.4353879606331
⁴√n	5.3835632709553
⁵√n	3.8446415681585

Divisors of 840

1, 2, 4, 7, 8, 14, 15, 28, 30, 56, 60, 105, 120, 210, 420, 840

16 divisors

τ	Total Divisors	16	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-839	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.0625	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	16	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 840 can be divided by 16 positive divisors. The sum of these divisors (counting 840) is 1, the average is 0.0625.

Base conversion 840

Base	System	Value
2	Binary	1101001000
3	Ternary	1011010
4	Quaternary	31020
5	Quinary	11330
6	Senary	3520
8	Octal	1510
10	Decimal	840
12	Duodecimal	5a0
16	Hexadecimal	348
20	Vigesimal	220
36	Base36	nc

Cryptographic Hash Functions

md5	fa83a11a198d5a7f0bf77a1987bcd006
sha1	c1d2fb848010807be783ec66dd6ddfad6863dbe7
sha256	fd0f7e53c5b02b688a57ee37f3d52065cb168a7b9fd5a3abd93d37e1559fbd30
sha512	f2af688d11a6b10a46b4068a2d2b7f443284f44e0a2158dc17a479a5e1587eb82262fc3484ee2967389fd8fe77898654ade5a87428797e25d29419d4b97bf7d9
ripemd-160	d84b9014f763b5d32652b58d663c15d1c3c20713

840 as geometric shapes

Circle

Radius = n

Diameter	1680
Circumference	5277.8756580309
Area	2216707.776373

Sphere

Radius = n

Volume	2482712709.5377
Surface area	8866831.1054918
Circumference	5277.8756580309

Square

Length = n

Perimeter	3360
Area	705600
Diagonal	1187.9393923934

Cube

Length = n

Surface area	4233600
Volume	592704000
Space diagonal	1454.9226783579

Equilateral Triangle

Length = n

Perimeter	2520
Area	305533.76245515
Altitude	727.46133917893

Triangular Pyramid

Length = n

Surface area	305533.76245515
Volume	69850836.272732
Height	395.97979746447