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Solve the following arithmetic problems and identify pairs of prime and coprime numbers.

Mathematics

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Answers

2 parts
a

19, 29\text{19, 29}

b

(4, 9)\text{(4, 9)}

Step-by-step solution

6 steps

Here are the solutions to the problems:

Part (و): Subtraction

37058−2346937058 - 23469
  1. Subtract the numbers.

    37058−23469=1358937058 - 23469 = 13589

    The result is 13589\boxed{\text{13589}}.

    Part (ہ): Addition

    33216+2859033216 + 28590
  2. Add the numbers.

    33216+28590=6180633216 + 28590 = 61806

    The result is 61806\boxed{\text{61806}}.

    Part (ج): Division

    8526÷138526 \div 13
  3. Perform the division.

    When 8526 is divided by 13:
    The quotient is 655.
    The remainder is 11.
    So, 8526=13×655+118526 = 13 \times 655 + 11.
    The result is 655 remainder 11\boxed{\text{655 remainder 11}}.

    Part (ن): Multiplication

    327×92327 \times 92
  4. Multiply 327 by 2.

    327×2=654327 \times 2 = 654

  5. Multiply 327 by 90.

    327×90=29430327 \times 90 = 29430

  6. Add the results from Step 1 and Step 2.

    654+29430=30084654 + 29430 = 30084
    The result is 30084\boxed{\text{30084}}.


    Question 4:

    a) Two prime numbers whose unit digit is 9.
    A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
    Two prime numbers ending in 9 are:

    • 19 (divisors are 1, 19)
    • 29 (divisors are 1, 29) Other examples include 59, 79, 89. The two numbers are 19, 29\boxed{\text{19, 29}}.

    b) Any pair of coprime numbers.
    Coprime numbers (or relatively prime numbers) are two integers whose greatest common divisor (GCD) is 1. This means they share no common positive factors other than 1.
    One pair of coprime numbers is:

    • (4, 9) The factors of 4 are {1, 2, 4}. The factors of 9 are {1, 3, 9}. The only common factor is 1, so their GCD is 1. Another example is (2, 3). The pair of numbers is (4, 9)\boxed{\text{(4, 9)}}.
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