Question

Найдите наибольший общий делитель чисел способом разложения на простые множители : 16 и 45;

Answer 1

16=2*2*2*2; 45=3*3*5; НОД(16;45)=1; 16 и 45 взаимно простые числа;

Answer 2

Finding the Greatest Common Divisor (GCD) by Prime Factorization

To find the greatest common divisor (GCD) of two numbers, 16 and 45, we can use the method of prime factorization. Prime factorization involves breaking down each number into its prime factors and then finding the common factors.

Let's find the prime factorization of 16 and 45:

- Prime factorization of 16: 16 = 2 * 2 * 2 * 2 = 2^4 - Prime factorization of 45: 45 = 3 * 3 * 5 = 3^2 * 5

Now, let's find the common factors by looking at the prime factors:

- The common factors are the prime factors that both numbers share. In this case, the common factor is 3.

Therefore, the greatest common divisor (GCD) of 16 and 45 is 3.

Conclusion

The greatest common divisor (GCD) of 16 and 45, found using the method of prime factorization, is 3.