Question

Find the last two digits of 273^1961

Answer 1

Answer:

the answer is infinite..

Answer 2

Answer:

73

Step-by-step explanation:

In order to determine last 2 digits of 273^1961.

We need to consider last 2 digits of expression 73^1961 since digits before 73 has no role in last 2 digits. This means last 2 digits will be same for 73^1961  or 273^1961 or 2273^1961 or 12373^1961 and so on.

Now, let us consider 73^1961

73^1961 = 73¹⁹⁶⁰ₓ 73¹

73^1961 = (73⁴)⁴⁹⁰ ₓ 73¹

73^1961 = (5329²)⁴⁹⁰ ₓ 73¹

5329² will have same last 2 digits as 29². So we will consider the expression as

(29²)⁴⁹⁰ ₓ 73¹

(841)⁴⁹⁰ ₓ 73¹

(841)⁴⁹⁰ will have same last 2 digits as (41)⁴⁹⁰. So we will consider the expression as

(41)⁴⁹⁰ₓ 73¹

(41)⁴⁹⁰ will have unit place of 1. Ten's place will be product of tens place digit of base and unit place digit of power = 4 x 0 = 0. So last 2 digits will be 01.

So expression will be 01 x 73 = 73

So last digit will be 73.