Rajasthan Computer Anudeshak Bharti 2026 | Maths Class – संख्या पद्धति (Number System) Part 07

Main ideas / lessons conveyed

• Rule of Divisibility as a calculation shortcut: The speaker emphasizes that divisibility rules let you “cut” numbers mentally by checking conditions on digits, instead of performing full long division.

• Rules build in families (related divisors): For example, 2 → 4 → 8 → 16 is treated as a progression where each next rule examines one more set of trailing digits.

• Digit-based tests:

  • Some rules depend on specific trailing digits (e.g., 2, 4, 8, 16, 25).
  • Some depend on the sum of digits (e.g., 3, 9).
  • Some depend on the unit digit only (e.g., 5).
  • 11 depends on alternating digit sums.

• Solving exam-style questions using these rules: The session includes multiple MCQs and missing-digit problems to practice applying the rules.

• If a rule isn’t given, you can derive it (“extra rules”):

  • If you don’t know a divisor rule (like 6, 18, 99), factor the divisor and combine known rules for coprime factors.

• Special patterns:

  • Repetition of digits/blocks can guarantee divisibility (e.g., repeated 2-digit patterns for 101, and repeated digit patterns six times relating to 3·7·11·13·37).

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Methodology / instruction lists (detailed)

A) Rules discussed for divisibility (core section)

• Rule for 2

  • Check the unit digit.
  • If the unit digit is 0 or 2 or divisible by 2, then the whole number is divisible by 2.

• Rule for 4

  • Check the last two digits (units + tens).
  • If the last two digits are 0, 4, 8, 12, … (i.e., divisible by 4), then the number is divisible by 4.

• Rule for 8

  • Check the last three digits (units + tens + hundreds).
  • If the last three digits are divisible by 8, then the number is divisible by 8.

• Rule for 16

  • By the progression pattern, check the last four digits.
  • If the last four digits are divisible by 16, then the number is divisible by 16.
  • (The speaker explains the pattern via 2 → 4 → 8 → 16, using examples mainly for 2, 4, 8.)

• Rule for 3

  • Compute the sum of all digits.
  • If the digit sum is divisible by 3, then the number is divisible by 3.

• Rule for 9

  • Compute the sum of all digits.
  • If the digit sum is divisible by 9, then the number is divisible by 9.
  • Key relationship emphasized:
    • If divisible by 9 ⇒ divisible by 3
    • Not vice versa (divisible by 3 does not guarantee divisibility by 9)

• Rule for 5

  • Check the unit digit.
  • If the unit digit is 0 or 5, then the number is divisible by 5.

• Rule for 25

  • Check the last two digits.
  • If the last two digits are divisible by 25, then the number is divisible by 25.
  • Note: two-digit multiples of 25 are limited to 25, 50, 75 (then applied conceptually to larger numbers).

• Rule for 8 in practice

  • For MCQs, compare candidates by applying the last three digits divisible by 8 test.

• Rule for 11 (explicitly taught later)

  • Split digits into alternating groups (alternating positions).
  • Compute the sum of digits in each group.
  • The number is divisible by 11 if:
    • the two sums are equal, or
    • their difference is divisible by 11.
  • (“Alternate” means skipping one digit each time—alternating positions.)

• Rule for 4 (as used in examples)

  • Uses the unit + tens (last two digits) test.

• Rule for 6

  • The speaker starts an approach based on factoring (“extra rules”), and also uses the idea that divisibility by 6 can be checked by ensuring divisibility by 2 and 3 together.

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B) “Extra rules” / derivation approach when a rule is not known

• If you don’t know a divisor’s specific rule:

  • Factor the divisor into smaller factors.
  • Apply known divisibility rules for those factors.
  • Ensure the split uses coprime (mutually non-overlapping) pieces (i.e., no shared/common factors between pieces).

• Examples of the approach (as described):

  • To test divisibility by 6:
    • Use 6 = 2 × 3
    • If the number satisfies the rules for 2 and 3, then it is divisible by 6.
  • For 18:
    • Use something like 18 = 2 × 9 (or an equivalent decomposition following the “no shared factors between pieces” instruction)
    • Apply rules for 2 and 9.
  • For composite divisors like 24, 48, 72, 99:
    • Factor and apply corresponding divisibility rules to the resulting coprime factors.

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C) Special rules based on repeating patterns

• Special rule for 101

  • If any two-digit number is repeated twice to form a four-digit pattern like ABAB,
  • Then the number is divisible by 101.

• Special rule for 3·7·11·13·37 (and related repetition)

  • If a number (or block) is repeated six times (or structured as a multiple of six repetitions),
  • Then it becomes divisible by 3, 7, 11, 13, and 37.
  • The key memorization product stated:
    • 3 · 7 · 11 · 13 · 37
  • The speaker also clarifies a block repetition example (repeating a group of digits six times).

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D) Worked-question methodology (how questions are solved)

• For MCQs like: “Which number is divisible by 8 / not divisible by 8 / divisible by 9?”

  • Apply the corresponding rule quickly to each option:
    • By 8: check last three digits
    • By 9: check sum of digits
    • By 3: check sum of digits
    • By 11: use alternating digit sums (or their difference)

• For missing digit / wildcard questions:

  • Determine how the divisibility condition restricts the missing digit(s).
  • Test candidate values until the divisibility condition is satisfied.
  • Use constraints efficiently—often by checking nearest values after a computed digit-sum remainder.

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Speakers / sources featured

• Primary speaker / instructor: “Tri Master ji” (referred to directly by viewers and as the teacher in subtitles)

• Mentioned attendees/viewers (not primary speakers):

  • D Kumar, Neelam ji, Rihanna ji, Ramesh ji, Rachna ji, Chaudhary sahab, Ramdhar ji sahab, Dharka sahab, Santosh ji, Anil Jakhar ji, Vicky ji