Solve (2^16+1)(2^4+1)(2^2+1)

$$( { 2 }^{ 16 } +1)( { 2 }^{ 4 } +1)( { 2 }^{ 2 } +1)$$

Evaluate

$$5570645$$

Solution Steps

Calculate 2 to the power of 16 and get 65536.

$$\left(65536+1\right)\left(2^{4}+1\right)\left(2^{2}+1\right)$$

Add 65536 and 1 to get 65537.

$$65537\left(2^{4}+1\right)\left(2^{2}+1\right)$$

Calculate 2 to the power of 4 and get 16.

$$65537\left(16+1\right)\left(2^{2}+1\right)$$

Add 16 and 1 to get 17.

$$65537\times 17\left(2^{2}+1\right)$$

Multiply 65537 and 17 to get 1114129.

$$1114129\left(2^{2}+1\right)$$

Calculate 2 to the power of 2 and get 4.

$$1114129\left(4+1\right)$$

Add 4 and 1 to get 5.

$$1114129\times 5$$

Multiply 1114129 and 5 to get 5570645.

$$5570645$$

Factor

$$5\times 17\times 65537$$