Math Question: What is the sum of the multiples of 61, starting from 61 up to and including 2017?

To find the required sum, we can use the formula for the sum of an arithmetic sequence: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, a is the first term, n is the number of terms, and d is the common difference. Since 61 is the first term and the common difference is also 61, we can plug in the values. Here, a = 61, n = (2017-61)/61+1 = 33, and d = 61. Substituting these values, we get Sn = (33/2)(2 * 61 + (33-1) * 61) = 33 * (122 + 32*61) = 33 * (122 + 1952) = 33 * 2074 = 68342. Therefore, the sum of the multiples of 61, from 61 up to and including 2017, is 68342.

Question: Four friends each bought an equal number of apples. If they altogether had 61 apples, how many apples did each friend buy?

Let's assume each friend bought x number of apples. Therefore, 4x = 61. Solving this equation gives us x = 61/4 = 15.25. Since we cannot have a fraction of an apple, it means each friend bought 15 apples.

Math question: What is the sum of the numbers from 61 to 120 inclusive, excluding multiples of 5?

To find the sum, start by calculating the number of terms to be added: (120 - 61) / 5 = 11. Now, the sum of an arithmetic series, S = (n / 2)(first term + last term), with n being the number of terms. The first term is 61, and the last term can be found by adding (n - 1) multiplied by the common difference, which is 5 for our case. The last term = 61 + (11 -1) * 5 = 115. Substituting values into our formula, S = (11 / 2)(61 + 115) = (11/2)(176) = 11 × 88 = 968. Therefore, the sum of the numbers from 61 to 120 (excluding multiples of 5) is 968.

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

61 (number)

61 is an odd 2-digits prime number following 60 and preceding 62. In scientific notation, it is written as 6.1 × 10^1. The sum of its digits is 7. It has a total of 1 prime factors and 2 positive divisors. There are 60 positive integers (up to 61) that are relatively prime to 61.

Interesting facts

61 has 2 divisors, whose sum is 62
The reverse of 61 is 16
Previous prime number is 1

Basic properties

Is Prime? yes
Number parity odd
Number length 2
Sum of Digits 7
Digital Root 7

Name

Name	sixty-one

Notation

Scientific notation	6.1 × 10^1
Engineering notation	6.1 × 10^0

Prime Factorization of 61

Prime Factorization 61

Composite number

ω	Distinct Factors	1	Total number of distinct prime factors
Ω	Total Factors	1	Total number of prime factors
rad	Radical	61	Product of the distinct prime numbers

The prime factorization of 61 is 61. Since it has a total of 1 prime factors.

Most popular turbo-numbers

4, 7, 84, 37, 748, 855, 1623, 5780, 65645, 17762, 928197, 151877, 8240109, 212080, 15690240, 83355239, 786742533, 37307224, 9862773880, 2831247589

Basic calculations (n = 61)

Multiplication

n×y

n×2	122
n×3	183
n×4	244
n×5	305

Division

n÷y

n÷2	30.5
n÷3	20.333333333333
n÷3	15.25
n÷5	12.2

Exponentiation

n^y

n²	3721
n³	226981
n⁴	13845841
n⁵	844596301

Nth Root

^y√n

²√n	7.8102496759067
³√n	3.9364971831022
⁴√n	2.7946823926712
⁵√n	2.2754430321145

Divisors of 61

1, 61

2 divisors

τ	Total Divisors	2	Total number of the positive divisors of n
σ	Sum of Divisors	62	Sum of all the positive divisors of n
s	Aliquot Sum	1	Sum of the proper positive divisors of n
A	Arithmetic Mean	31	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	7.8740078740118	Returns the nth root of the product of n divisors
H	Harmonic Mean	1.9677419354839	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 61 can be divided by 2 positive divisors. The sum of these divisors (counting 61) is 62, the average is 31.

Base conversion 61

Base	System	Value
2	Binary	111101
3	Ternary	2021
4	Quaternary	331
5	Quinary	221
6	Senary	141
8	Octal	75
10	Decimal	61
12	Duodecimal	51
16	Hexadecimal	3d
20	Vigesimal	31
36	Base36	1p

Cryptographic Hash Functions

md5	7f39f8317fbdb1988ef4c628eba02591
sha1	6c1e671f9af5b46d9c1a52067bdf0e53685674f7
sha256	d029fa3a95e174a19934857f535eb9427d967218a36ea014b70ad704bc6c8d1c
sha512	00819bedf0933e1d682112566d00541fa0ebcdbfda053ee2399bb9d51da4ea809b9ca4252ed318b0046fc43ef66853ff2872e2fd894bf371f6683a15bdaaee74
ripemd-160	1bc842a94797571b8073d2d7d555f287c66b0b18

61 as geometric shapes

Circle

Radius = n

Diameter	122
Circumference	383.27430373795
Area	11689.866264008

Sphere

Radius = n

Volume	950775.78947262
Surface area	46759.46505603
Circumference	383.27430373795

Square

Length = n

Perimeter	244
Area	3721
Diagonal	86.267027304759

Cube

Length = n

Surface area	22326
Volume	226981
Space diagonal	105.6550992617

Equilateral Triangle

Length = n

Perimeter	183
Area	1611.2402637409
Altitude	52.827549630851

Triangular Pyramid

Length = n

Surface area	1611.2402637409
Volume	26749.967383417
Height	28.755675768253