Math question: What is the least prime number greater than 992 that when divided by 3 leaves a remainder of 1, a remainder of 2 when divided by 4, and a remainder of 3 when divided by 5?

To find the least prime number satisfying the given conditions, let's analyze each requirement. Considering the remainder of 1 when divided by 3 implies the number is congruent to 1 modulo 3. Similarly, the requirements of remainder 2 modulo 4 and 3 modulo 5 imply the number is congruent to 2 modulo 4 and 3 modulo 5, respectively. By combining these congruences, we can create the following equation: n ≡ 1 (mod 3) n ≡ 2 (mod 4) n ≡ 3 (mod 5) To solve this system, the Chinese Remainder Theorem can be applied. By examining the modulo values, we find n ≡ 11 (mod 60). Now, we can list the prime numbers greater than 992 and find the least one congruent to 11 modulo 60. Prime numbers greater than 992: 997, 1009, 1013, 1019, 1021... Combining this list with our congruence, we notice that the least prime number satisfying these conditions is 1019. Thus, the answer is the prime number 1019.

Question: What is the largest prime factor of the number 992?

To find the largest prime factor of 992, we start by dividing it by the smallest prime number, 2. The result is 496. We proceed to divide 496 by 2 again, giving us 248. Dividing this by 2, we get 124, then 62, 31, where we notice that 31 is a prime number. So, the largest prime factor of 992 is 31.

Question: What is the result when the number 992 is divided by the sum of its digits, multiplied by 3, subtracted by the square root of the number 992, and then added to twice the cube of its digits?

To calculate this, we first find the sum of the digits of 992, which is (9 + 9 + 2 = 20). Next, we divide 992 by this sum, giving us (992 ÷ 20 = 49.6). Multiplying this quotient by 3, we get (49.6 * 3 = 148.8). Now, subtracting the square root of 992, which approximates to (√992 ≈ 31.46), we have (148.8 - 31.46 = 117.34). Finally, we cube each digit of 992 (9³ = 729, 9³ = 729, 2³ = 8), double the sum (2 * (729 + 729 + 8) = 2932), and add it to the previous result, obtaining (117.34 + 2932 = 3049.34). Thus, the answer is approximately 3049.34.

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

992 (number)

992 is an even 3-digits composite number following 991 and preceding 993. In scientific notation, it is written as 9.92 × 10^2. The sum of its digits is 20. It has a total of 6 prime factors and 12 positive divisors. There are 480 positive integers (up to 992) that are relatively prime to 992.

Interesting facts

992 has 12 divisors, whose sum is 2016
The reverse of 992 is 299
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 3
Sum of Digits 20
Digital Root 2

Name

Name	nine hundred ninety-two

Notation

Scientific notation	9.92 × 10^2
Engineering notation	9.92 × 10^0

Prime Factorization of 992

Prime Factorization 2 × 2 × 2 × 2 × 2 × 31

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	6	Total number of prime factors
rad	Radical	62	Product of the distinct prime numbers

The prime factorization of 992 is 2 × 2 × 2 × 2 × 2 × 31. Since it has a total of 6 prime factors.

Most popular turbo-numbers

2, 5, 43, 62, 738, 861, 5043, 2953, 86770, 50747, 947053, 411686, 8470754, 1581661, 29990924, 83604535, 972572609, 953252564, 1006080507, 9171398548

Basic calculations (n = 992)

Multiplication

n×y

n×2	1984
n×3	2976
n×4	3968
n×5	4960

Division

n÷y

n÷2	496
n÷3	330.66666666667
n÷3	248
n÷5	198.4

Exponentiation

n^y

n²	984064
n³	976191488
n⁴	968381956096
n⁵	960634900447232

Nth Root

^y√n

²√n	31.496031496047
³√n	9.9732619044773
⁴√n	5.6121325265934
⁵√n	3.9746815093289

Divisors of 992

1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992

12 divisors

τ	Total Divisors	12	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-991	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.083333333333333	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	12	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 992 can be divided by 12 positive divisors. The sum of these divisors (counting 992) is 1, the average is 0.083333333333333.

Base conversion 992

Base	System	Value
2	Binary	1111100000
3	Ternary	1100202
4	Quaternary	33200
5	Quinary	12432
6	Senary	4332
8	Octal	1740
10	Decimal	992
12	Duodecimal	6a8
16	Hexadecimal	3e0
20	Vigesimal	29c
36	Base36	rk

Cryptographic Hash Functions

md5	860320be12a1c050cd7731794e231bd3
sha1	fad3ea4094a1e0792528fd5419b68db5ce72e603
sha256	c0d2d188feaa1562d9a1ca041b28896773ad5cf55793d9c056a2ece46eb3667a
sha512	1e0cc1fae10f391abadeb1afa840d3f56ca349c9afbe1b3023b3f627a20c83ae5cd1d92267d1baf2507daf6740c43a8312de57a51cb23616d393566b488a6bc3
ripemd-160	05497c53a5f07e3a00ec93cd8b923be3b0be6fe3

992 as geometric shapes

Circle

Radius = n

Diameter	1984
Circumference	6232.9198247221
Area	3091528.2330622

Sphere

Radius = n

Volume	4089061342.9303
Surface area	12366112.932249
Circumference	6232.9198247221

Square

Length = n

Perimeter	3968
Area	984064
Diagonal	1402.8998538741

Cube

Length = n

Surface area	5904384
Volume	976191488
Space diagonal	1718.1944011083

Equilateral Triangle

Length = n

Perimeter	2976
Area	426112.21147486
Altitude	859.09720055416

Triangular Pyramid

Length = n

Surface area	426112.21147486
Volume	115045270.15023
Height	467.6332846247