If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?
A) 23
B) 20
C) 11
D) 5
E) 2
OA is a
What is the correct answer here how do you arrive at it? please help me out.
Thanks
Prime factors/number properties
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Hi Roland2rule,If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?
A) 23
B) 20
C) 11
D) 5
E) 2
OA is a
What is the correct answer here how do you arrive at it? please help me out.
Thanks
Let's take a look at your question.
Since, {x} is the product of all even integers from 1 to x inclusive, therefore we can write {22} as,
$$\left\{22\right\}=22\times20\times18\times16\times...\times2$$
Similarly {20} can be written in product form as:
$$\left\{20\right\}=20\times18\times16\times...\times2$$
Now we are asked to find the greatest prime factor of {22}+{20}. For this purpose let's find the sum first.
$$\left\{22\right\}+\left\{20\right\}=\left(22\times20\times18\times16\times...\times2\right)+\left(20\times18\times16\times...\times2\right)$$
Factor out (20 x 18 x 16 x .. x 2), we get
$$\left\{22\right\}+\left\{20\right\}=\left(20\times18\times16\times...\times2\right)\left(22+1\right)$$
$$\left\{22\right\}+\left\{20\right\}=\left(20\times18\times16\times...\times2\right)23$$
Now we can see all the factors of {22}+{20}, Except 23 which is a prime factor, all other factors are even integers that are not prime.
Therefore, the greatest prime factor of {22}+{20} is 23.
Option A is correct.
Hope it helps.
I am available if you'd like any follow up.
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{22} = 22 x 20 x 18 x 16 x ... 4 x 2BTGmoderatorRO wrote:If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?
A) 23
B) 20
C) 11
D) 5
E) 2
OA is a
What is the correct answer here how do you arrive at it? please help me out.
Thanks
{20} = 20 x 18 x 16 x ... 4 x 2
{22} + {20} = (22 x 20 x 18 x 16 x ... 4 x 2) + (20 x 18 x 16 x ... 4 x 2)
From the two terms above, we pull out the common factor of (20 x 18 x 16 x ... 4 x 2), yielding:
{22} + {20} = 20 x 18 x 16 x ... 4 x 2 x (22 + 1)
{22} + {20} = 20 x 18 x 16 x ... 4 x 2 x 23
We see that the greatest prime factor is 23.
Answer: A
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Now if \(\{x\}\) is the product of all even integers from 1 to \(x\) inclusive, this meansBTGmoderatorRO wrote:If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {22} + {20}?
A) 23
B) 20
C) 11
D) 5
E) 2
OA is a
What is the correct answer here how do you arrive at it? please help me out.
Thanks
we can take 20 common from \(\{22\} + \{20\}\)
\(20\times 18 \cdots 2 (22 + 1)\)
\(23 \times \) Some expression
23 \(\Rightarrow\) __A__.
Greatest prime factor.