1. Find the unit digit of product of all odd prime numbers.
Sol:
We know that if we multiply by 5 to any odd prime number the result will always give unit digit 5.
Hence required unit digit will be 5. Answer
2. Find the unit digit of 583 × 782 ×216 × 424
Sol:
3. Find the unit digit of product of all even numbers.
Sol:
Some of the starting even numbers are:
2, 4, 6, 8, ⑩, 12, 14, …………
Zero multiplied by any number gives result zero.
Hence required number = 0 Answer
4. Find the unit digit of 5!
Sol:
Hence we can say any factorial number greater than or equal to 5! has unit digit as Zero.
5. Find the unit digit of 4!
Sol:
4! = 4 × 3 × 2 × 1 = 24 ⟶ 4 Answer
6. Find the unit digit of (3952)³⁷¹⁹
Sol:
\(\frac{{3719}}{4}\) ⟶ R = 3
∴ Uₔ = (2)³ = 8 Answer
7. Find the unit digit of (80076526)⁴⁶⁶⁵²
Sol:
Since Uₔ of base is 6
∴ Uₔ of number = 6 Answer
8. Find the unit digit of (490087054)³⁹²⁰⁵⁸⁴
Sol:
\(\frac{{39020584}}{4}\) ⟶ R = 0
& base has Uₔ 4 i.e. even
∴ Uₔ of given numbers = 6
9. Find unit digit of (2.34589)¹⁰⁵⁹
Sol:
\(\frac{{1059}}{4}\) ⟶ R = 3
base Uₔ = 9
∴ Uₔ of number = (9)³ = 9 Answer
10. Find the unit digit of (8908050225)⁵⁸⁹⁴
Sol:
Since base has Uₔ = 5
Hence Uₔ of number = 25 Answer