Question

What is the greatest prime factor of 4​

Answer 1

CORRECT QUESTION

What is the greatest prime factor of 4¹⁷ - 2²⁸

ANSWER

The answer is 7

GIVEN

Mathematical operation: 4¹⁷ - 2²⁸

TO FIND

Greatest prime factor of the given expression.

SOLUTION

We can simply solve the above problem as follows;

We are given,

4¹⁷ - 2²⁸

We can also write it as;

(2²)¹⁷ - 2²⁸

Applying- (mᵃ)ᵇ = mᵃˣᵇ

= 2³⁴ - 2²⁸

Taking 2²⁸ as common

= 2²⁸ (2⁶ - 1)

Now,

We know that the prime factors of 2²⁸ = 2

So simplifying

2⁶ - 1

= 64-1 = 63

Factors of 63 = 3 × 3 × 7

Hence, The greatest prime factor is 7.

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Answer 2

Answer:

$2 * 2$

Step-by-step explanation:

As an even composite number, the number four can be factored further as the product of the numbers two and two. Therefore, $4$ can be expressed as $2*2$. Therefore, $2*2$ or $2^{2}$ is the prime factorization of $4$.

The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. That can be divided into two components. The number 4 is not a prime. It's referred to as a composite number. The answer is 2 times 2 equals 4, and since these 2s are truly prime numbers, we can circle them if we split these things out. We may then state that the prime factorization of 20 actually equals 2 times 2 times 5 in total. And you're not need to perform the 4x5 method always. You might divide 20 into two multiples of ten. Whatever way you like is OK. Thus, notice that 2 multiplied by 10 is prime whereas 10 is composite. We can divide that into 2 times 5 to get the total. Therefore, we are circling every prime number we come across. Again, we have 2 times 2 times 5, which equals 20. That's how prime factorization works.

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