Question

find the greatest number that will exactly divide 840 and 2296

Answer 1

Here is your answer

Answer 2

Answer:

The greatest number that exactly divide 840 and 2296 is 56.

Step-by-step explanation:

Given the two numbers: 840 and 2296

Need to find the greatest number that exactly divide both the numbers, 840 and 2296.

The number that exactly divides both the numbers is the greatest common divisor(GCD).

So, let us find the GCD(840, 2296) by prime factorization method.

The prime factorization of 840 is

$2\times 2\times2 \times 3\times5\times 7~\mbox{or}~\underline{2^3} \times 3^1\times5^1\times \underline{7^1}$

The prime factorization of 2296 is

$2\times 2\times2\times 7\times 41~\mbox{or}~\underline{2^3} \times \underline{7^1}\times 41^1$

So, the common factors in both the numbers are the underlined numbers.

Thus,  $\mbox{GCD}(840, 2296)={2^3} \times {7^1}=8 \times7=56$

Therefore, the greatest number that exactly divide 840 and 2296 is 56.

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