Question

33^24 - 17^24 is at least divisible by


option
26
80
800
50​

Answer 1

Step-by-step explanation:the answer is to be 6,000 into 400/6

Answer 2

The expression $33^{24}-17^{24}$ is at least divisible by 50 (last option).

Given,

The expression: $33^{24}-17^{24}$.

To Find,

The number by which the given expression is divisible.

Solution,

The method of finding the number by which the expression is divisible is as follows -

We know that $a^2-b^2=(a-b)(a+b)$ and $a^3+b^3=(a+b)(a^2-ab+b^2)$.

Now we will simplify the expression by using the above formulas.

$33^{24}-17^{24}=(33^{12})^2-(17^{12})^2=(33^{12}-17^{12})(33^{12}+17^{12})$

$=((33^{6})^2-(17^{6})^2)(33^{12}+17^{12})=(33^6-17^6)(33^6+17^6)(33^{12}+17^{12})$

$=((33^3)^2-(17^3)^2)(33^6+17^6)(33^{12}+17^{12})$

$=(33^3+17^3)(33^3-17^3)(33^6+17^6)(33^{12}+17^{12})$

$=(33+17)(33^2-33*17+17^2)(33^3-17^3)(33^6+17^6)(33^{12}+17^{12})$

$=50*(33^2-33*17+17^2)(33^3-17^3)(33^6+17^6)(33^{12}+17^{12})$

So we can observe that there is a factor of 50 in the expression.

So the expression is divisible by 50.

Hence, the expression $33^{24}-17^{24}$ is at least divisible by 50 (last option).

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