Question

What is the units digit in the product (8^17 x 4^12 x 9419)?
Select one:
a. 3
b. 2
c. 4
d. 1

Answer 1

Answer:

A number is made up from digits in the numeral system is called Unit's Digit. We often use the decimal system in which we use 10 digits, In writing the any number, many digits are used, even repeatation of digits. when we write any number using the digits, the last digit ( from right side ) in that number is called unit digit. For example in the number 48750, here "0" is called unit digit.

Now, the product of unit digits in the given product 459×46×25×28@×484 is shown below:

$$9\times 6\times 5\times @\times 4=216\times@$$

Now, it is given that the unit digit is 2, so, to obtain 2 in the unit's place, let @=7 (because 6×7=42), then we have:

216×@=216×7=1512 where 2 is the unit digit.

Hence, the digit place of @ is 7.

Step-by-step explanation:

I hope it will help you

Answer 2

Concept:

If the difference between two integers a and b is a multiple of n, we say that they are "congruent modulo n." 184 and 51, for instance, are congruent modulo 19 because 184 - 51 = 133 = 719, while 17 and 5 are equivalent modulo 3 because 17 - 5 = 12 = 43. This is frequently expressed as 17 ≡ 5 mod 3 or 184 ≡  51 mod 19. The phrase "negative 8 is congruent to 10 modulo 9," or occasionally "negative 8 is congruent to 10 mod 9," is pronounced "-8 ≡  10 mod 9."

Using congruence modulo theorem,

a≡ k ( mod n)

where, a = dividend

           k = remainder

           b= divisor

Given:

8¹⁷ x 4¹² x 9419

Find:

What is the units digit in the product 8¹⁷ x 4¹² x 9419

Solution:

8¹⁷ = 2³ˣ¹⁷ =2⁵¹

   2≡ 2 (mod 10)

⇒ 2³ ≡  8 ≡ -2 ( mod 10)

2⁹ ≡ -8 ≡ 2 (mod 10)

2⁹ˣ⁵ ≡ (2)⁵ ≡ 32   (mod 10)

2⁴⁵ ≡ 2 (mod 10)

2⁴⁵ˣ⁶ ≡ 2 x 2⁶ (mod 10)

2⁵¹ ≡ 128 ( mod 10)

2⁵¹ ≡ 8 (mod 10)

Again,

4¹² = 2²⁴

⇒ 2 ≡ 2 (mod 10)

2³ ≡  -2 (mod 10)

2⁹ ≡ 8 ≡ -2 (mod 10)

2¹⁸ ≡ 4 (mod 10)

2¹⁸ x 2⁶ ≡ 4 x 2⁶ (mod 10)

2²⁴ ≡ 256 ( mod 10)

2²⁴ ≡ 6 (mod 10)

Again,

8 x 6 x 9419 ≡  48 x 9419 ( mod 10)

8 x 6 x 9419 ≡ 8 x 9 ( mod 10)

8 x 6 x 9419 ≡ 72 ( mod 10)

8 x 6 x 9419 ≡ 2 ( mod 10)

Therefore, the unit  digit in the product is 2

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