What is the greatest prime factor of 422+752+6300

Question

What is the greatest prime factor of  42^2+75^2+6300

a) 3
b) 7
c) 11
d) 13
e) 79

KarishmaB · Accepted Answer

First, take out whatever common number you can find:

42^2+75^2+6300 = 3^2 * (14^2 + 25^2 + 700)

Now, you may actually know these squares so calculations are a little easier. Of course, it will be great if you can identify that 2*14*25 = 700

= 3^2 * ( 14 + 25)^2 = 3^2 * 39^2 = 3^2 * 3^2 * 13^2

So 13 is the greatest prime factor.

mvictor · Answer

is there a faster way than squaring all the numbers?

42^2 = (50-8)(50-8) = 1764
75^2 = (100-25)(100-25) = 5625

1764+5625+6300 = 13689
this number is divisible by 3 and 9

divide by 9 and get 1521, the sum of this number is again a multiple of 9, thus we can divide it one more time by 9. we get 169, and 169 is 13^2. thus the answer is 13.

ynaikavde · Answer

Hint

A^2+ B^2+2*AB

Bunuel · Answer

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Alex75PAris · Answer

Thanks !!

6300 = 2 * 42* 75 So 42^2 + 75^2 + 6300 = (42+75)^2 = 117^2 = (9*13)^2 So 13

stonecold · Answer

Great Question.
There are Two ways to do this =>
First Method 
Recognise 2*42*75=6300
hence 42^2+75^2+6300= (42+75)^2= 117^2 => 3^4 *13^2 => Greatest Prime factor =13
Second method

Go Traditional way. Open the brackets and get to work.
Lets see

N=42^2+75^2+6300
N=(2*3*7)^2 + (5^2*3)^2 + 2^2*3^2*5^2*7
N=2^2*3^2*7^2 + 5^4*3^2 +2^2*3^2*5^2*7
N=3^2 
N=3^2*1521
N=3^2*3^2*169
N=3^4*13^2
Greatest Prime factor is 13

Personally i like the second method.

Hence D

law258 · Answer

42^2 + 75^2 + 6300 = 13689

13689 --> 3x4563 ....169 = 13^2

Thus, the correct answer is D.

KanishkM · Answer

Always remember to simplify

42^2+75^2+6300

2^2 3^2 7^2 + 3^2 5^4 + 7 * 3^2 2^2 5^2

take  3^2  common out

3^2 ( 7^2 2^2 + 5^2  )

3^2 ( 196 + 25 * 53)

3^2 ( 1521)

3^2 3^2 13^2

Highest will be 13

D

ScottTargetTestPrep · Answer

Consider the perfect square (a + b)^2, which expands to a^2 + b^2 + 2ab.

This pattern can be applied to (42 + 75)^2, which expands to 42^2 + 75^2 + 2(42)(75). Note that the third term of this expansion 2(42)(75) = 6300. Thus, we see that 42^2 + 75^2 + 6300 = (42 + 75)^2. Now, perform the addition inside the parentheses, obtaining 117^2 = (3^2 x 13)^2. We see that the greatest prime factor is 13.

Answer: D

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What is the greatest prime factor of 422+752+6300

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What is the greatest prime factor of 422+752+6300

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