Divisibility test

 Tests for Divisibility

Divisibility Tests	Example
A number is divisible by 2  if the last digit is 0, 2, 4, 6 or 8.	178 is divisible by 2 since the last digit is 8.
A number is divisible by 3  if the sum of the digits is divisible by 3.	138 is divisible by 3 since the sum of the digits is 15 (1+3+8=12), and 12 is divisible by 3.
A number is divisible by 4  if the number formed by the last two digits is divisible by 4.	312 is divisible by 4 since 12 is divisible by 4.
A number is divisible by 5  if the last digit is either 0 or 5.	295 is divisible by 5 since the last digit is 5.
A number is divisible by 6  if it is divisible by 2 and it is divisible by 3.	168 is divisible by 6 since it is divisible by 2  and it is divisible by 3.
A number is divisible by 8  if the number formed by the last three digits is divisible by 8.	8,120 is divisible by 8 since 120 is divisible by 8.
A number is divisible by 9  if the sum of the digits is divisible by 9.	540 is divisible by 9 since the sum of the digits is 18 (5+4+0=9), and 9 is divisible by 9.
A number is divisible by 10  if the last digit is 0.	1,370 is divisible by 10 since the last digit is 0.

Examples.

Example 1:	Determine whether 150 is divisible by 2, 3, 4, 5, 6, 9 and 10.
	150 is divisible by 2 since the last digit is 0.
	150 is divisible by 3 since the sum of the digits is 6 (1+5+0 = 6), and 6 is divisible by 3.
	150 is not divisible by 4 since 50 is not divisible by 4.
	150 is divisible by 5 since the last digit is 0.
	150 is divisible by 6 since it is divisible by 2 AND by 3.
	150 is not divisible by 9 since the sum of the digits is 6, and 6 is not divisible by 9.
	150 is divisible by 10 since the last digit is 0.

Example 2:	Determine whether 225 is divisible by 2, 3, 4, 5, 6, 9 and 10.
	225 is not divisible by 2 since the last digit is not 0, 2, 4, 6 or 8.
	225 is divisible by 3 since the sum of the digits is 9, and 9 is divisible by 3.
	225 is not divisible by 4 since 25 is not divisible by 4.
	225 is divisible by 5 since the last digit is 5.
	225 is not divisible by 6 since it is not divisible by both 2 and 3.
	225 is divisible by 9 since the sum of the digits is 9, and 9 is divisible by 9.
	225 is not divisible by 10 since the last digit is not 0.

Example 3:	Determine whether 7,168 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10.
	7,168 is divisible by 2 since the last digit is 8.
	7,168 is not divisible by 3 since the sum of the digits is 22, and 22 is not divisible by 3.
	7,168 is divisible by 4 since 168 is divisible by 4.
	7,168 is not divisible by 5 since the last digit is not 0 or 5.
	7,168 is not divisible by 6 since it is not divisible by both 2 and 3.
	7,168 is divisible by 8 since the last 3 digits are 168, and 168 is divisible by 8.
	7,168 is not divisible by 9 since the sum of the digits is 22, and 22 is not divisible by 9.
	7,168 is not divisible by 10 since the last digit is not 0 or 5.

Example 4:	Determine whether 35,120 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10.
	35,120 is divisible by 2 since the last digit is 0.
	35,120 is not divisible by 3 since the sum of the digits is 11, and 11 is not divisible by 3.
	35,120 is divisible by 4 since 20 is divisible by 4.
	35,120 is divisible by 5 since the last digit is 0.
	35,120 is not divisible by 6 since it is not divisible by both 2 and 3.
	35,120 is divisible by 8 since the last 3 digits are 120, and 120 is divisible by 8.
	35,120 is not divisible by 9 since the sum of the digits is 11, and 11 is not divisible by 9.
	35,120 is divisible by 10 since the last digit is 0. Divisibility by 11     A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.(This abstract and confusing sounding rule is much clearer with a few examples)  Use the divisibility calculator below to determine if any number is divisible by eleven. Type in any number that you want, and the calculator will explain whether or not it's divisible by 11 based on this rule.

A number is divisible by 13 if the following is true:

• Multiply the ones digit by 4.
• Add this value from the rest of the number.
• Continue this pattern until you find a number you know is or is not divisible by 13.

Example        3159 is divisible by 13 because

a) 9 x 4 = 36.

b) 315  + 3 6 = 351 
c) 1 x 4  = 4
d)  35 + 4 = 39  which is divisible by 13.

Example        22113 is divisible by 13 because

a) 3 x 4 = 12.

b) 2211  +12  =   2223 
c) 3 x 4  = 12
d)  222 + 12 = 234
e) 4x 4 = 16
f)  23 + 16 = 39   which is divisible by 13.

Famous Mathematics Quotes by Great Mathematician

Famous Mathematics Quotes by                

Great  Mathematician

Albert Einstein (1879-1955)

• So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality.
• I don't believe in mathematics.
• God does not care about our mathematical difficulties. He integrates empirically.
• Nature to him (Newton) was an open book, whose letters he could read without effort.
• Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.
• Do not worry about your difficulties in mathematics, I assure you that mine are greater.

Archimedes of Syracus (287-212 B. C. E)

• Give me a place to stand, and I will move the earth.
• Eureka, euraka!
• Don't spoil my circles! (or Do not disturb my circles!)
• There are things which seem incredible to most men who have not studied Mathematics.

Aristotle (384-322 B. C. E)

• Now what is characteristic of any nature is that which is best for it and gives most joy. Such a man is the life according to reason, since it is that which makes him man.
• There is nothing strange in the circle being the origin of any and every marvel.
• The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.
• To Thales the primary question was not what do we know, but how do we know it.
• If this is a straight line [showing his audience a straight line drawn by a ruler], then it necessarily ensues that the sum of the angles of the triangle is equal to two right angles, and conversely, if the sum is not equal to two right angles, then neither is the triangle rectilinear.
• It is not once nor twice but times without number that the same ideas make their appearance in the world.
• But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end.
• We cannot ... prove geometrical truths by arithmetic.
• The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
• The continuum is that which is divisible into indivisibles that are infinitely divisible. Physics.

"Mathematics is the door and key to the Sciences"

                                                                        Roger Bacon (1214-1294)