1. What is the least number that must be added to 1056 so the number is divisible by 23?

2. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?

3. If HCF (1008, 20) = HCF (20, a) = HCF (a, b) where 1008=20×q+a; 20=a×m+b where (q, a)and (m, b) are positive integers satisfying Euclid’s Division Lemma. What could be the values of a and b?

4. If the number 91876y2 is completely divisible by 8, then the smallest whole number in place of y will be:

5. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?

6. Find the HCF of 1848, 3058 and 1331.

7. Which of the following does not satisfy the following property?
A number that divides 542 and 128 and leaves a remainder 2 in both cases.

8.

9. Euclid’s division lemma states “Given positive integers a and b, there exist unique integers q and r satisfying a=bq+r”. Which of the following is true for r?

10.