Question

Представить произведение 37×1001 в виде произведения простых множителей

Answer 1

1001*37 = 7*11*13*37
отв 37037

Answer 2

Factoring 37 × 1001 into Prime Factors

To express the product of 37 × 1001 as a product of prime factors, we need to find the prime factors of both numbers and then multiply them together.

Let's start by finding the prime factors of 37 and 1001.

Prime factors of 37: 37 is a prime number, which means it is only divisible by 1 and itself. Therefore, the prime factorization of 37 is simply 37 itself.

Prime factors of 1001: To find the prime factors of 1001, we can use various methods such as trial division or prime factorization algorithms. One way to find the prime factors is to divide 1001 by prime numbers starting from 2 and continuing until the quotient is 1.

Dividing 1001 by 2 gives us a quotient of 500 with a remainder of 1. Since 2 does not divide evenly into 1001, we move on to the next prime number, which is 3.

Dividing 1001 by 3 gives us a quotient of 333 with a remainder of 2. Again, 3 does not divide evenly into 1001, so we continue with the next prime number, which is 5.

Dividing 1001 by 5 gives us a quotient of 200 with a remainder of 1. 5 does not divide evenly into 1001, so we move on to the next prime number, which is 7.

Dividing 1001 by 7 gives us a quotient of 143 with a remainder of 0. 7 divides evenly into 1001, so we can conclude that 7 is a prime factor of 1001.

Now that we have found the prime factors of both 37 and 1001, we can multiply them together to express the product of 37 × 1001 as a product of prime factors.

The prime factorization of 37 is simply 37 itself.

The prime factorization of 1001 is 7 × 11 × 13.

Therefore, the prime factorization of 37 × 1001 is 37 × 7 × 11 × 13.

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