What is the largest prime number that can be evenly divided by the sum of its digits when represented in base 10, given that the number lies between 1977 to 1979 (inclusive)?

To determine the largest prime number meeting the criteria, we analyze the three numbers. Starting with 1977, the sum of its digits is 1 + 9 + 7 + 7 = 24. However, 1977 itself is not prime since 3 divides evenly into it (3 * 659 = 1977). Moving on to 1978, the digit sum is 1 + 9 + 7 + 8 = 25. But 1978 is divisible by 2 (2 * 989 = 1978), thus not prime. Lastly, taking 1979, the digit sum is 1 + 9 + 7 + 9 = 26. Since no factors divide evenly into 1979, it satisfies the prime condition. Hence, 1979 is the largest prime number between 1977 and 1979, making it the answer.

Math Question: What is the sum of the squares of the prime factors of 1977?

To find the prime factors of 1977, we start by dividing it successively with prime numbers. We find 23 as a prime factor twice since 1977 divided by 23 is 86, and 86 divided by 23 is 3. Hence, the prime factors are 23 and 23. The sum of the squares of these prime factors is calculated as (23^2) + (23^2) = 1156 + 1156 = 2312. The sum of the squares of the prime factors of 1977 is 2312.

Math question: What is the sum of the factors of 1977? Solution: To find the factors of 1977, we need to determine all the numbers that divide evenly into it. Starting with 1 and going up to 1977, we find that 1, 3, 659, and 1977 are the factors. Calculating their sum: 1 + 3 + 659 + 1977 = 2640.

The sum of factors of 1977 is 2640. Factors help us understand the number's divisibility. For instance, 1977 can be divided by 1, 3, 659, and 1977 without leaving a remainder. Factors are crucial in prime factorization, determining common multiples, and simplifying fractions. Moreover, the sum of factors can help analyze the number's properties. Here, 2640 suggests that 1977 is an abundant number, exceeding the sum of its proper divisors (sum of factors excluding 1977 itself). Exploring such number characteristics aids in various mathematical investigations and applications.

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

1977 (number)

1977 is an odd 4-digits composite number following 1976 and preceding 1978. In scientific notation, it is written as 1.977 × 10^3. The sum of its digits is 24. It has a total of 2 prime factors and 4 positive divisors. There are 1316 positive integers (up to 1977) that are relatively prime to 1977.

Interesting facts

1977 has 4 divisors, whose sum is 2640
The reverse of 1977 is 7791
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 4
Sum of Digits 24
Digital Root 6

Name

Name	one thousand nine hundred seventy-seven

Notation

Scientific notation	1.977 × 10^3
Engineering notation	1.977 × 10^3

Prime Factorization of 1977

Prime Factorization 3 × 659

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	2	Total number of prime factors
rad	Radical	1977	Product of the distinct prime numbers

The prime factorization of 1977 is 3 × 659. Since it has a total of 2 prime factors.

Most popular turbo-numbers

3, 8, 54, 65, 65, 593, 2421, 5212, 74212, 68524, 707695, 680753, 3229720, 7682506, 3251096, 52232546, 548165106, 726619060, 7756761655, 8195369447

Basic calculations (n = 1977)

Multiplication

n×y

n×2	3954
n×3	5931
n×4	7908
n×5	9885

Division

n÷y

n÷2	988.5
n÷3	659
n÷3	494.25
n÷5	395.4

Exponentiation

n^y

n²	3908529
n³	7727161833
n⁴	15276598943841
n⁵	30201836111973657

Nth Root

^y√n

²√n	44.463468150831
³√n	12.550727194997
⁴√n	6.6680932920012
⁵√n	4.5624837836515

Divisors of 1977

1, 3, 659, 1977

4 divisors

τ	Total Divisors	4	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-1976	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.25	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	4	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 1977 can be divided by 4 positive divisors. The sum of these divisors (counting 1977) is 1, the average is 0.25.

Base conversion 1977

Base	System	Value
2	Binary	11110111001
3	Ternary	2201020
4	Quaternary	132321
5	Quinary	30402
6	Senary	13053
8	Octal	3671
10	Decimal	1977
12	Duodecimal	1189
16	Hexadecimal	7b9
20	Vigesimal	4ih
36	Base36	1ix

Cryptographic Hash Functions

md5	4afd521d77158e02aed37e2274b90c9c
sha1	15afd7262ebd18f6f7c1401f13249c2afd747402
sha256	576c85c584f60555c2a024cbb99dfbbdb5f58c3bdcf28dbc8ea315fd46a388f3
sha512	1868b2485269e3ad2f33ca9f800c82c56d3453db2dfe61f5a08eb9998892b7e28ab16f533e6aeef29a29865c5af0508f8043bc3602ca05c9aea9dfa063592946
ripemd-160	d5a929b89eba3ae20109c7d388e700e86f6eb942

1977 as geometric shapes

Circle

Radius = n

Diameter	3954
Circumference	12421.857352294
Area	12279005.992743

Sphere

Radius = n

Volume	32367459796.87
Surface area	49116023.970971
Circumference	12421.857352294

Square

Length = n

Perimeter	7908
Area	3908529
Diagonal	2795.9002128116

Cube

Length = n

Surface area	23451174
Volume	7727161833
Space diagonal	3424.2644465637

Equilateral Triangle

Length = n

Perimeter	5931
Area	1692442.7027141
Altitude	1712.1322232818

Triangular Pyramid

Length = n

Surface area	1692442.7027141
Volume	910654755.24003
Height	931.96673760387