Solve (2^{1}+1)(2^{2}+1)(2^{4}+1)(2^8+1)(2^16+1)(2^32+1)(2^61+1)

$$( 2 ^ { 1 } + 1 ) ( 2 ^ { 2 } + 1 ) ( 2 ^ { 4 } + 1 ) ( 2 ^ { 8 } + 1 ) ( 2 ^ { 16 } + 1 ) ( 2 ^ { 32 } + 1 ) ( 2 ^ { 61 } + 1 )$$

Evaluate

$$42535295865117307949062726993466884095$$

Solution Steps

Calculate 2 to the power of 1 and get 2.

$$\left(2+1\right)\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Add 2 and 1 to get 3.

$$3\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Calculate 2 to the power of 2 and get 4.

$$3\left(4+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Add 4 and 1 to get 5.

$$3\times 5\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Multiply 3 and 5 to get 15.

$$15\left(2^{4}+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Calculate 2 to the power of 4 and get 16.

$$15\left(16+1\right)\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Add 16 and 1 to get 17.

$$15\times 17\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Multiply 15 and 17 to get 255.

$$255\left(2^{8}+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Calculate 2 to the power of 8 and get 256.

$$255\left(256+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Add 256 and 1 to get 257.

$$255\times 257\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Multiply 255 and 257 to get 65535.

$$65535\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Calculate 2 to the power of 16 and get 65536.

$$65535\left(65536+1\right)\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Add 65536 and 1 to get 65537.

$$65535\times 65537\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Multiply 65535 and 65537 to get 4294967295.

$$4294967295\left(2^{32}+1\right)\left(2^{61}+1\right)$$

Calculate 2 to the power of 32 and get 4294967296.

$$4294967295\left(4294967296+1\right)\left(2^{61}+1\right)$$

Add 4294967296 and 1 to get 4294967297.

$$4294967295\times 4294967297\left(2^{61}+1\right)$$

Multiply 4294967295 and 4294967297 to get 18446744073709551615.

$$18446744073709551615\left(2^{61}+1\right)$$

Calculate 2 to the power of 61 and get 2305843009213693952.

$$18446744073709551615\left(2305843009213693952+1\right)$$

Add 2305843009213693952 and 1 to get 2305843009213693953.

$$18446744073709551615\times 2305843009213693953$$

Multiply 18446744073709551615 and 2305843009213693953 to get 42535295865117307949062726993466884095.

$$42535295865117307949062726993466884095$$

Factor

$$3^{2}\times 5\times 17\times 257\times 641\times 65537\times 6700417\times 768614336404564651$$