Divisible by 7
Double last digit and subtract from rest.
Rule:
Rest β (2 Γ Last Digit)
Example:
203 β 20 β (2Γ3)=14 β
Divisible by 8
Last 3 digits divisible by 8
Rule:
Check last 3 digits
Example:
512 β 512 Γ· 8 β
Divisible by 9
Sum of digits divisible by 9
Rule:
Digit sum Γ· 9
Example:
729 β 7+2+9=18 β
Divisible by 11
Difference of odd-even place digits
Rule:
(Odd β Even) = 0 or 11
Example:
121 β (1+1)β2=0 β
Divisible by 13
Add 4Γlast digit to rest
Rule:
Rest + (4 Γ Last Digit)
Example:
286 β 28+24=52 β
π Practice Questions
Q1. Check if 301 is divisible by 7.
301 β 30β2 = 28 β
Q2. Check if 4096 is divisible by 8.
096 Γ· 8 = 12 β
Q3. Check if 567 is divisible by 9.
5+6+7=18 β
Q4. Check if 1331 is divisible by 11.
(1+3)-(3+1)=0 β
Q5. Check if 247 is divisible by 13.
24+28=52 β
π Practice Questions
Q1. Is 456 divisible by 3?
Answer: Yes (4+5+6=15)
Q2. Is 128 divisible by 4?
Answer: Yes (28 Γ· 4)
Q3. Is 75 divisible by 5?
Answer: Yes (Last digit 5)
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π Remainder Theorem
Concept β’ Flow β’ Examples β’ Practice
Dividend
β¬
Divisor Γ Quotient
β¬
Remainder
β
Concept
When a number is divided, we get:
Dividend = Divisor Γ Quotient + Remainder
Remainder is always less than divisor.
π Example
17 Γ· 5 = 3 remainder 2
17 = 5 Γ 3 + 2
π Practice
Q1. Find remainder when 29 is divided by 6.
Show Answer
29 = 6 Γ 4 + 5
β Remainder = 5
Q2. Find remainder when 245 is divided by 8.
Show Answer
245 = 8 Γ 30 + 5
β Remainder = 5