Unlock the secrets of quick mental math with divisibility rules. This blog explores simple yet powerful tricks to determine if a number is divisible by 2, 3, 5, 7, and more—without long division. Perfect for students, competitive exam aspirants, and math enthusiasts. Our easy-to-follow explanations and examples will sharpen your number sense. Whether you’re solving math problems faster or just curious about number patterns, this post is your go-to guide for mastering divisibility rules effortlessly!
Divisibility by 2: If Last digit of the number is divisible by 2
Divisibility by 4: If Last two digits of the number are divisible by 4
Divisibility by 8: If Last three digits of the number are divisible by 8
Divisibility by 16: If Last four digits of the number are divisible by 16
Divisibility by 32: If Last five digits of the number are divisible by 32
Divisibility of 3: All such numbers the Sum of whose digits are divisible by 3
Divisibility of 9: All such numbers the Sum of whose digits are divisible by 9
Divisibility by 6: A number is divisible by 6 if it is simultaneously divisible by 2 and 3
Divisibility by 5: If Last digit (0 and 5) is divisible by 5
Divisibility by 25: If Last two digits of the number are divisible by 25
Divisibility by 125: If Last three digits of the number are divisible by 125
Divisibility by 7: Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, then so was the original number.
Divisibility by 11: The difference of the sum of the digits in the odd places and the sum of digits in the even places is ‘0’ or multiple of 11 is divisible.
Divisibility by 3, 7, 11, 13, 21, 37 and 1001:
(A) If any number is made by repeating a digit 6 times the number will be divisible by 3, 7, 11, 13, 21, 37 and 1001 etc.
(B) A six digit number if formed by repeating a three digit number; for example, 256, 256 or 678, 678 etc. Any number of this form is always exactly divisible by 7, 11, 13, 1001 etc.
Some important points:
(A) If a is divisible by b then ac is also divisible by b.
(B) If a is divisible by b and b is divisible by c then a is divisible by c.
(C) If n is divisible by d and m is divisible by d then (m + n) and (m – n) are both divisible by d. This has an important implication. Suppose 28 and 52 are both divisible by 4. Then (52 + 28) as well as (52 – 28) are divisible by 4.
(D) a^n-b^n, when n is even number is divisible by ( a+b) & (a-b) both.
(E) a^n-b^n, when n is odd number is divisible by (a-b).
(F) a^n+b^n, when n is odd number is divisible by (a+b).
Thanks for visiting. Always keep practicing.
