Math question: Find a two-digit number that is divisible by 7, 8, and 3.

To find a two-digit number that is divisible by 7, 8, and 3, we can start by finding the least common multiple (LCM) of these numbers. The LCM of 7, 8, and 3 is 168, as it is the smallest number that is divisible by all three. Hence, 168 satisfies the given conditions. To verify, we can check its divisibility. Dividing 168 by 7, we get 24; dividing by 8, we get 21; and dividing by 3, we get 56. So, indeed 168 is divisible by 7, 8, and 3.

Math Question: If you multiply a number by 168 and then subtract it by 57, the result is equal to twice the number, what is the number?

Let's assume the number is x. According to the given condition, we can form the equation 168x - 57 = 2x. Simplifying, we get 166x = 57. Dividing both sides by 166, we find x ≈ 0.343. Therefore, the number that satisfies the condition is approximately 0.343.

Question: What is the smallest positive integer n such that the remainder when n is divided by 7, 9, and 12 will all be 6?

To find the smallest positive integer with remainders of 6 when divided by 7, 9, and 12, let's apply the Chinese Remainder Theorem. First, let's find the LCM of the divisors (7, 9, and 12), which is 252. We now have the equation n ≡ 6 (mod 7), n ≡ 6 (mod 9), and n ≡ 6 (mod 12). Next, we'll solve each congruence separately. For n ≡ 6 (mod 7), the solution is n = 6 + 7k, where k is an integer. Similarly, for n ≡ 6 (mod 9), n = 6 + 9j. Lastly, for n ≡ 6 (mod 12), n = 6 + 12m. Now, let's combine these equations to find a solution that satisfies all three congruences. We have: 6 + 7k = 6 + 9j = 6 + 12m Simplifying this, we get: 7k = 9j = 12m Now, let's find the least common multiple of 7, 9, and 12, which is 252. We have: 252/7 = 36, 252/9 = 28, 252/12 = 21 Therefore, 252 is the least common multiple of 7, 9, and 12, and it satisfies the given congruences. Hence, the smallest positive integer n is 252.

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

168 (number)

168 is an even 3-digits composite number following 167 and preceding 169. In scientific notation, it is written as 1.68 × 10^2. The sum of its digits is 15. It has a total of 5 prime factors and 16 positive divisors. There are 48 positive integers (up to 168) that are relatively prime to 168.

Interesting facts

168 has 16 divisors, whose sum is 480
The reverse of 168 is 861
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 3
Sum of Digits 15
Digital Root 6

Name

Name	one hundred sixty-eight

Notation

Scientific notation	1.68 × 10^2
Engineering notation	1.68 × 10^0

Prime Factorization of 168

Prime Factorization 2 × 2 × 2 × 3 × 7

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	5	Total number of prime factors
rad	Radical	42	Product of the distinct prime numbers

The prime factorization of 168 is 2 × 2 × 2 × 3 × 7. Since it has a total of 5 prime factors.

Most popular turbo-numbers

7, 8, 34, 26, 154, 787, 1858, 6319, 60869, 9650, 395603, 55807, 1603250, 8996102, 22638544, 57387347, 620673411, 604202015, 8692125859, 1728667171

Basic calculations (n = 168)

Multiplication

n×y

n×2	336
n×3	504
n×4	672
n×5	840

Division

n÷y

n÷2	84
n÷3	56
n÷3	42
n÷5	33.6

Exponentiation

n^y

n²	28224
n³	4741632
n⁴	796594176
n⁵	133827821568

Nth Root

^y√n

²√n	12.961481396816
³√n	5.5178483527622
⁴√n	3.6002057436785
⁵√n	2.7865180227312

Divisors of 168

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

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	-167	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 168 can be divided by 16 positive divisors. The sum of these divisors (counting 168) is 1, the average is 0.0625.

Base conversion 168

Base	System	Value
2	Binary	10101000
3	Ternary	20020
4	Quaternary	2220
5	Quinary	1133
6	Senary	440
8	Octal	250
10	Decimal	168
12	Duodecimal	120
16	Hexadecimal	a8
20	Vigesimal	88
36	Base36	4o

Cryptographic Hash Functions

md5	006f52e9102a8d3be2fe5614f42ba989
sha1	f76b2ea6b45eff3bc8e4399145cc17a0601f5c8d
sha256	80c3cd40fa35f9088b8741bd8be6153de05f661cfeeb4625ffbf5f4a6c3c02c4
sha512	e0b163e4414d0090558b64908866c553e71f8c3aba2cd482d5e1490b8ab6362b3b3c6a2648c316cd94347a53bfa4ef998295b241e55f71d678914bcc94022945
ripemd-160	86ad6511e9728abb5449658c8239671879de8381

168 as geometric shapes

Circle

Radius = n

Diameter	336
Circumference	1055.5751316062
Area	88668.311054918

Sphere

Radius = n

Volume	19861701.676302
Surface area	354673.24421967
Circumference	1055.5751316062

Square

Length = n

Perimeter	672
Area	28224
Diagonal	237.58787847868

Cube

Length = n

Surface area	169344
Volume	4741632
Space diagonal	290.98453567157

Equilateral Triangle

Length = n

Perimeter	504
Area	12221.350498206
Altitude	145.49226783579

Triangular Pyramid

Length = n

Surface area	12221.350498206
Volume	558806.69018186
Height	79.195959492893