Prime Numbers

To express 600 as a product of prime factors, we can factor it as follows: 600 = 2 × 300 = 2 × 2 × 150 = 2 × 2 × 2 × 75 = 2^3 × 3 × 25 = 2^3 × 3 × 5 × 5. Therefore, the prime factorization of 600 is 2^3 × 3^1 × 5^2.

The group of numbers that includes all prime numbers is 3 and 11. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 1 is not considered a prime number. Thus, the prime numbers in the given group are 3 and 11.

To find the prime factors of a number, first check if it is odd or even.

If even it will divide by '2' , the first prime number.

Since '62' is even it will divide by '2' .

Hence

2)62

The answer is '31'

'31' is also a prime number , so divide by itself, to arrive at an answer of '1'.

31)31

=1

So the Prime factors of '62' are 2, & 31.

NB When testing for prime factors. Check if the number is 'odd' ( 1,3,5,7,9)

or even ( 2,4,6,8,0) These are the suffix digits of any given number.

If even then it will divide by '2' , and keep on dividing by '2' until an odd number answer. Then test for '3' , then '5' , then ;7; et seq., until you arrive at '1'.

All the dividing numbers(quotients) are the prime factors.

NNB Some little 'tricks' . If a number ends in '5' or '0' it will divide by '5'

e.g. 10155 will divide by '5'

If the digits add to '9' , then it will divide by '9'.

e.g. 189 ; 1 + 8 + 9 = 18 => 1 + 8 = 9 will divide by '9'

Only '3' & '7' must be fully tested by division for the prime factors.

The first prime numbers , up to '20' are : - 2,3,5,7,11,13,17, & 19.

The largest single digit prime is '7'

The largest two digit prime is '97'.

Their product is

97 X 7 = 679.

Single digit primes are ;- 2,3,5,7,

7 > 5

Answer; '7'.

The prime number between 20 and 30 whose ones digit is 7 greater than its tens digit is 23. The tens digit is 2, and the ones digit is 3, which is 7 greater than 2. Additionally, 23 is a prime number because it is only divisible by 1 and itself, with no other factors.

Prime numbers between 60 and 100 are ,

61,67, 71, 73, 79, 83, 87, 89, 91, 97,

Answer '71'. Because 7 - 1 = 6.

To find the prime factorization of 360, we can divide it by the smallest prime number, which is 2.

1. (360 \div 2 = 180)
2. (180 \div 2 = 90)
3. (90 \div 2 = 45)
4. (45 \div 3 = 15)
5. (15 \div 3 = 5)
6. (5 \div 5 = 1)

Thus, the prime factorization of 360 is (2^3 \times 3^2 \times 5^1).

The number 405 can be factored into its prime components as follows: 405 = 5 × 3^4. Therefore, the different prime factors of 405 are 5 and 3. This means that 405 has a total of 2 different prime factors.

The set of even counting numbers includes all positive integers that are divisible by 2, such as 2, 4, 6, 8, and so on. This set is infinite and can be expressed mathematically as {2n | n ∈ ℕ}, where ℕ represents the set of natural numbers. Therefore, the set of even counting numbers is a well-defined subset of the natural numbers.

A composite index calculates an overall measure by combining multiple individual indices or metrics into a single value, often used to assess performance, economic indicators, or market trends. It typically incorporates various factors, allowing for a more comprehensive analysis than any single index could provide. This approach helps in identifying patterns or trends that may not be evident when examining individual components separately. Composite indices are commonly used in finance, economics, and social research.

The prime numbers between 14 and 36 are 17, 19, 23, 29, 31. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself.

Two numbers are considered relatively prime if their greatest common divisor (GCD) is 1. The GCD of 100 and 202 is 2, since both numbers share this factor. Therefore, 100 and 202 are not relatively prime.

Composite numbers are natural numbers greater than one that have more than two distinct positive divisors, meaning they can be divided evenly by numbers other than one and themselves. For example, 4, 6, and 9 are composite numbers because they can be divided by 1, themselves, and at least one other number (like 2 for 4, or 3 for 9). In contrast, prime numbers, such as 2, 3, and 5, have exactly two distinct positive divisors: 1 and themselves.

'98' is a COMPOUND Number.

Compound numbers are the product of the multiplication of two( or more) smaller numbers.

2 x 49 = 98 ( So '98' is a compound number)

NB Any even number , except '2' , is a compound number.

Even numbers are those that end in 0,2,4,6,8

NNB Prime numbers always, except '2' itself, end in an odd number, except '5'.

So e.g.

1,000,002 is Compound, it ends in '2' . It is NOT prime.

1,000,000,015 is a compound number, because it ends in '5'. The odd number exception.

'7' IS a Prime Number.

NO it is NOT a Prime number.

It is a multiple of '13'

11999 / 13 = 923

That is

923 x 13 = 11999

A composite sample is a collection of multiple individual samples combined to represent a larger population or area. This approach is often used in environmental monitoring, quality control, and research to obtain a more accurate assessment of variability and trends. By averaging the characteristics of the individual samples, a composite sample provides a more comprehensive overview while minimizing the impact of outliers.

A prime motivation for Russia's colonial expansion in the late 19th and early 20th centuries was the desire for economic resources and strategic access to new markets. This period was marked by intense competition among imperial powers, and Russia sought to secure its influence in Asia and the Pacific, particularly in areas like Manchuria and the Far East. Additionally, nationalism and the belief in the civilizing mission further fueled expansionist ambitions, as Russia aimed to spread its culture and authority.

Prim remembers her mother, who was a healer and deeply connected to their community's traditions. Her mother often recited prayers and teachings from their religion, instilling in Prim a sense of compassion and responsibility. Additionally, Prim may recall the reverence for figures like the Avox, who symbolize sacrifice and endurance in their society.

The term "composite" refers to a number that has more than two distinct positive divisors, meaning it can be divided evenly by numbers other than 1 and itself. The digit "2" in the ones place is not a composite number; it is actually a prime number because its only divisors are 1 and 2. Therefore, when discussing the ones place, the digit "2" does not qualify as composite.

The prime factorization of 40 is found by breaking it down into its prime components. It can be expressed as (40 = 2^3 \times 5). This means that 40 is made up of three 2s and one 5 as its prime factors.

The prime factorization of 180 is obtained by dividing the number by its smallest prime factors. It can be expressed as ( 180 = 2^2 \times 3^2 \times 5^1 ). This means 180 can be broken down into the prime factors 2, 3, and 5, with 2 appearing twice, 3 appearing twice, and 5 appearing once.

what is the greatest multiple of 4 which is less than 100?

19 and 19