What Are The Prime Factors Of 700 Weegy

< p > The prime factors of 700 are the numbers that, when multiplied together, equal 700. In other words, they are the building blocks of 700. The prime factors of 700 are 2, 2, 5, and 7. This is because 700 can be written as the product of these numbers: 700 = 2 x 2 x 5 x 7. < p >

< p > The prime factors of a number can be found by dividing the number by successively smaller prime numbers until the quotient is 1. For example, to find the prime factors of 700, we can divide it by 2 to get 350, and then divide 350 by 2 to get 175. We can then divide 175 by 5 to get 35, and finally divide 35 by 7 to get 5. The last number we get is 1, so we know that the prime factors of 700 are 2, 2, 5, and 7. < p >

What is a Prime Number?

Prime numbers are positive integers greater than 1 that have only two factors: 1 and themselves. For example, 2, 3, 5, 7, and 11 are prime numbers. 1 is not a prime number because it has only one factor, itself.

Prime numbers are important in cryptography because they are used to generate large numbers that are difficult to factor. For example, the RSA encryption algorithm uses prime numbers to generate encryption keys that protect data privacy.

Many methods can be used to find prime numbers. One common method is the sieve of Eratosthenes. The sieve of Eratosthenes is a simple algorithm that can be used to find all the prime numbers up to a given number n.

The sieve of Eratosthenes works by first creating a list of all the numbers from 2 to n. Then, the algorithm iterates over the list of numbers and crosses out all the numbers that are not prime. The numbers that are not crossed out are the prime numbers.

The sieve of Eratosthenes is not the only method used to find prime numbers. Several other methods, such as the Miller-Rabin primality test and the AKS primality test, are more efficient for testing the primality of large numbers.

What Are The Prime Factors Of 700?

The prime factors of 700 are 2, 2, 5, and 5. This means that 700 can be expressed as the product of these prime numbers: 2 x 2 x 5 x 5 = 700.

Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, and 11 are all prime numbers.

Prime Factorization

Prime factorization is the process of expressing a number as the product of its prime factors. For example, the prime factorization of 700 is 2 x 2 x 5 x 5.

How to find the prime factors of 700?

Prime factorisation is the process of breaking a number down into its prime factors, which are numbers that can only be divided by themselves and one. To find the prime factors of 700, we can follow these steps:

1. Divide by the smallest prime number

The smallest prime number is 2. We divide 700 by 2 and get 350.

2. Divide the result by the same prime number again

We can divide 350 by 2 again to get 175.

3. Continue dividing by the same prime number until it no longer divides evenly

We can divide 175 by 2 again to get 87.5. However, 87.5 is not an integer, so we stop dividing by 2.

4. Repeat the process with the next smallest prime number

The next smallest prime number is 5. We divide 87.5 by 5 to get 17.5. However, 17.5 is not an integer, so we stop dividing by 5.

5. Continue until the result is a prime number

The next smallest prime number is 7. We divide 17.5 by 7 to get 2.5. However, 2.5 is not an integer, so we stop dividing by 7.

6. The prime factors are the numbers that we divided by

In this case, the prime factors of 700 are 2, 2, 5, and 7. We can write this as:

700 = 2 x 2 x 5 x 7

The Prime Factors of 700

The prime factors of a number are the prime numbers whose multiplication results in the original number. So, to find the prime factors of 700, we need to find the prime numbers that divide 700 into a whole number.

**The prime factorization of 700 is 2^2 x 5^2 x 7 **

• 2 is a prime number and it divides 700 into 350.
• 350 is an even number, so it can be divided by 2 again, giving 175.
• 175 is also an odd number, so we need to find a different prime number to divide it with.
• 5 is a prime number and it divides 175 into 35.
• 35 is also an odd number, so we need to find a different prime number to divide it with.
• 7 is a prime number and it divides 35 into 5.
• 5 is a prime number, so we have found all the prime factors of 700.

Therefore, the prime factors of 700 are 2 x 2 x 5 x 5 x 7 = 700.

What is the greatest common factor of 700?

700 = 2^2 x 5^2 x 7

The greatest common factor of 700 is 100.

What is the least common multiple of 700?

The least common multiple (LCM) of two numbers is the smallest number that is divisible by both numbers.

To find the LCM of 700, we first need to find its prime factors. The prime factors of 700 are:

2 x 2 x 5 x 5 x 7 = 700

The LCM of 700 is the product of its prime factors, raised to the highest power that they occur in any of the prime factorizations of the numbers.

Therefore, the LCM of 700 is:

2² x 5² x 7 = 1400

So the least common multiple of 700 is 1400.

Conclusion

The prime factorization of 700 is 2² x 5² x 7. This means that 700 can be expressed as the product of these three prime numbers.

Prime factorization is a useful tool for understanding the structure of numbers. It can be used to find the greatest common factor and least common multiple of two or more numbers, and it can also be used to solve equations.

Frequently Asked Questions

What are the prime factors of 700?

The prime factors of 700 are 2, 2, 5, 5, and 7. This means that 700 can be expressed as the product of these prime numbers: 700 = 2 × 2 × 5 × 5 × 7.

How do you find the prime factors of a number?

To find the prime factors of a number, you can use a method called prime factorization. This involves repeatedly dividing the number by the smallest prime number that divides it until the quotient is 1. The prime numbers that you use to divide the number are the prime factors.

What is the largest prime factor of 700?

The largest prime factor of 700 is 7.

What are the factors of 700?

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700.

What is the prime factorization of 700 written in exponential form?

The prime factorization of 700 written in exponential form is: 700 = 2^2 × 5^2 × 7.