Советы от нейросети в категории prime factorization

Finding the НОК of a set of numbers

2024-02-15 18:56:46

The least common multiple (НОК) of a set of numbers is the smallest positive number that is divisible by all of the numbers in the set. To solve this problem, we first need to find the prime factorization of each number in the set. In this case, the prime factorization of 2 is 2, the prime factorization of 3 is 3, the prime factorization of 4 is 2^2, the prime factorization of 5 is 5, the prime factorization of 6 is 2 x 3, the prime factorization of 7 is 7, the prime factorization of 8 is 2^3, the prime factorization of 9 is 3^2, and the prime factorization of 10 is 2 x 5. Next, we need to find the highest power of each prime factor that appears in any of the numbers. In this case, the highest power of 2 is 3 (from 8), the highest power of 3 is 2 (from 9), the highest power of 5 is 1 (from 5 and 10), and the highest power of 7 is 1 (from 7). Now, we multiply all of these highest powers together to get the НОК(2, 3, 4, 5, 6, 7, 8, 9, 10) which is 2^3 x 3^2 x 5 x 7 = 2520.

Thus, your НОК(2, 3, 4, 5, 6, 7, 8, 9, 10) is 2520.

Finding the LCM of 40 and 16

2024-01-11 20:38:41

To solve this problem, you will need to find the least common multiple of 40 and 16. The least common multiple (LCM) is the smallest positive integer that is divisible by both numbers.

First, let's break down 40 and 16 into their prime factors.

40 = 2 * 2 * 2 * 5

16 = 2 * 2 * 2 * 2

The prime factorization of 40 has two 2s and a 5, while the prime factorization of 16 has four 2s. To find the LCM, we need to take the highest power of each prime factor. In this case, it would be four 2s and one 5.

Therefore, the LCM of 40 and 16 is 2 * 2 * 2 * 2 * 5 = 80.

So 80 is the smallest number that is divisible by both 40 and 16. Mission accomplished!

Simplify Fraction

2023-12-24 17:03:29

To simplify a fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. In this case, the GCF of 5 and 28 is 1, so we can divide both numbers by 1 to get the simplified form.

Therefore, the simplified fraction is 5*227/1*28 = 5*227/28 = 1135/28.

To shortcut the dividing process, we can use prime factorization method which breaks down the numbers into factors.

For the numerator 1135, the prime factorization is 5*227, while for the denominator 28, the prime factorization is 2*2*7. Then, we can cancel out common factors and simplify.

So, the simplified fraction is still 5*227/28 = 1135/28.

Finding the Least Common Multiple (LCM) of 270 and 450

2023-11-15 18:42:44

How to Find the Least Common Multiple (LCM) of 270 and 450?

The LCM of two numbers is the smallest positive number that is divisible by both of them. In order to find the LCM of 270 and 450, we need to follow these steps:

Write out the prime factorization of each number. Prime factorization means to break down a number into its prime factors. In this case, we have:

270 = 2 x 3 x 3 x 3 x 5
450 = 2 x 3 x 3 x 5 x 5

Identify the common prime factors and their highest powers. In this case, we have 2, 3 and 5 with the highest powers being 1, 3 and 3 respectively.
Multiply the highest powers of the common prime factors. In this case, we have (2^1)(3^3)(5^3) = 2 x 27 x 125 = 6750. Therefore, 6750 is the LCM of 270 and 450.
Check if 6750 is divisible by both 270 and 450. In this case, 6750 is indeed divisible by both numbers, confirming our answer.

Therefore, the LCM of 270 and 450 is 6750. Hope this explanation was helpful!

Finding the Greatest Common Divisor

2023-11-07 18:42:09

The greatest common divisor (НОД) of 1184 and 16 is 16. To find the НОД of two numbers, you need to factor both numbers and then find the common prime factors. In this case, the prime factorization of 1184 is 2^5 * 37 and the prime factorization of 16 is 2^4. Since 2 is the only common prime factor, the НОД is 2^4 or simply 16.