Question 33 of 36beginner🔧 ApplyNumerical4 marks

Find the remainders obtained when each of the following numbers are divided by i) 10, ii) 5, iii) 2. 78, 99, 173, 572, 980, 1111, 2345

Correct Answer

Rule: Remainder when dividing by 10 = last digit Remainder when dividing by 5 = last digit (if < 5), or last digit - 5 (if ≥\geq 5) Remainder when dividing by 2 = 0 if last digit is even, 1 if odd

78: Last digit = 8 i) By 10: 8 ii) By 5: 8 - 5 = 3 iii) By 2: 0 (even)

99: Last digit = 9 i) By 10: 9 ii) By 5: 9 - 5 = 4 iii) By 2: 1 (odd)

173: Last digit = 3 i) By 10: 3 ii) By 5: 3 iii) By 2: 1 (odd)

572: Last digit = 2 i) By 10: 2 ii) By 5: 2 iii) By 2: 0 (even)

980: Last digit = 0 i) By 10: 0 ii) By 5: 0 iii) By 2: 0 (even)

1111: Last digit = 1 i) By 10: 1 ii) By 5: 1 iii) By 2: 1 (odd)

2345: Last digit = 5 i) By 10: 5 ii) By 5: 0 iii) By 2: 1 (odd)

Exercise: Figure it Out (Section 6) | Q: 4 | (Page Page 20)
For More Understanding

Explanation

The remainder when dividing by 10 is the last digit. The remainder when dividing by 5 is the last digit if it's less than 5, otherwise last digit minus 5. The remainder when dividing by 2 is 0 if the last digit is even, 1 if odd.

Solution Steps

  1. Remainder when dividing by 10 = last digit

  2. Remainder when dividing by 5 = last digit (if < 5), or last digit - 5 (if ≥\geq 5)

  3. Remainder when dividing by 2 = 0 if last digit is even, 1 if odd

  4. 78: Last digit 8. By 10: 8. By 5: 8-5=3. By 2: 0 (even).

  5. 99: Last digit 9. By 10: 9. By 5: 9-5=4. By 2: 1 (odd).

  6. 173: Last digit 3. By 10: 3. By 5: 3. By 2: 1 (odd).

  7. 572: Last digit 2. By 10: 2. By 5: 2. By 2: 0 (even).

  8. 980: Last digit 0. By 10: 0. By 5: 0. By 2: 0 (even).

  9. 1111: Last digit 1. By 10: 1. By 5: 1. By 2: 1 (odd).

  10. 2345: Last digit 5. By 10: 5. By 5: 0. By 2: 1 (odd).

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