Divisibility · Topic 2 of 4

🔍 Find the Missing Digit

1 exam question type, fully solved

These questions hide one digit (shown as *, @, a letter, or a blank) and ask which value makes the whole number divisible. The skill is to pick the right rule and turn it into a single small equation in that unknown digit.

How to find the hidden digit

• Divisor 3 or 9: add the known digits, then choose the missing digit so the total is a multiple of 3 or 9. For the least digit, aim for the nearest multiple — e.g. if the known digits sum to 24, the next multiple of 9 is 27, so the missing digit is 3.

• Divisor 2, 5 or 10: only the last digit is fixed (even; 0 or 5; or 0).

• Divisor 4 or 8: only the last two or three digits matter, so you usually solve for a trailing digit.

• Composite divisor (18, 36, 72, …): split into co-prime factors and apply each rule. For example — the last-two-digit rule fixes one digit, the digit-sum rule the other.

Watch the wording: “least value” wants the smallest digit, and a digit can only be 0–9, so an option like 10 is never valid.

🔍Missing Digit FinderTest all 10 digits at once — no guessing

Number pattern (one digit hidden)

Must be divisible by

Rule of 9: the digit sum must be a multiple of 9. Known digits: 2 + 3 + 5 + 6 = 16. Now add the blank digit and test the total.

_ = 0 16 + 0 = 16 ✗

_ = 1 16 + 1 = 17 ✗

_ = 2 ✓16 + 2 = 18 ✓

_ = 3 16 + 3 = 19 ✗

_ = 4 16 + 4 = 20 ✗

_ = 5 16 + 5 = 21 ✗

_ = 6 16 + 6 = 22 ✗

_ = 7 16 + 7 = 23 ✗

_ = 8 16 + 8 = 24 ✗

_ = 9 16 + 9 = 25 ✗

Valid digit: 2 — e.g. 23256 ÷ 9 = 2584

For 234a56 to be divisible by 3, the known digits sum to ; the next multiple of 3 is 21, so .

Q1Find the least digit a so that 51a3 is divisible by 9.

Q2For 38a to be divisible by 6, the least value of a is:

Q3For 7a4 to be divisible by 9, what is a?

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Real exam questions — Find the Missing Digit

1 question types · 5 solved examples from real SSC papers

Match the divisor to its rule, then turn the rule into one equation in the unknown digit.

How to solve this type

Match the divisor to its rule and turn the rule into one equation in the unknown digit. For 3 or 9, the digit sum must be a multiple of 3 or 9. For 2, 5 or 10, only the last digit is fixed. For 4 or 8, only the last two or three digits matter. For a composite divisor like 18, 36 or 72, split it into co-prime factors and apply each rule. When the question asks for the LEAST digit, jump to the nearest multiple, not a higher one.

Find the value of a so that 234a56 is divisible by 3.

AAny of 0, 3, 6, 9B0C1D2

Find the least value of @ so that 7@5471 is divisible by 9.

A3B1C4D6

Find the least value of * so that 457643*4 is divisible by 18.

A9B5C4D3

If 7A425B is divisible by 36, what is A − B?

A0B5C2D1

If the 8-digit number 4432A43B is divisible by both 9 and 5, find A + B.

A12B7C5D8