The last four digits of the natural number 7100 are

Question

The last four digits of the natural number 7100 are (A) 2731 (B) 1301 (C) 2511 (D) 0001

Tardigrade Admin · Accepted Answer

7100 = 4950 = (50 - 1)50 = (1 - 10)50 = 1-50×50+(50⋅49/2)⋅(50)2-(50⋅49⋅48/6)⋅(50)3 + multiple of 104 = 1 - 2500 + 3062500 + multiple of 104 = 3060001 + multiple of 104 ∴ The last four digits are 0001.

Q. The last four digits of the natural number $7^{100}$ are

$2731$

$1301$

$2511$

$0001$

Q. The last four digits of the natural number 7100 are

2731

1301

2511

0001

7100=4950=(50−1)50=(1−10)50 =1−50×50+250⋅49​⋅(50)2−650⋅49⋅48​⋅(50)3 + multiple of 104 =1−2500+3062500+ multiple of 104 =3060001+ multiple of 104 ∴ The last four digits are 0001.

Q. The last four digits of the natural number $7^{100}$ are

$2731$

$1301$

$2511$

$0001$