Ask Math Expert


Home >> Math

Explain the rules of Divisibility ?

Divisible by 2: If the last digit is a 0, 2, 4, 6, or 8, the number is evenly divisible by 2.

Divisible by 2

Not Divisible by 2

4, 12, 1006, 88, 100

5, 13, 1007, 89, 101

Divisible by 3: Add together the digits. If the result is evenly divisible by 3 (in other words, if the result is a multiple of 3), so is the original number.

Example 1: Is the number 2553 divisible by 3?

Step 1: Add the digits together.
(2 + 5 + 5 + 3) = 15

Step 2: Does 3 evenly divide into 15?
(15 / 3 ) = 5

The answer is yes. So 2553 is divisible by 3.

Example 2: Is the number 2554 divisible by 3?

Step 1: Add the digits together.
(2 + 5 + 5 + 4) = 16

Step 2: Does 3 evenly divide into 16?
(16/ 3) = 5 R 1

The answer is no. So 2553 is not divisible by 3.
Example 3: Is the number 4,715,448,735,448 divisibly by 3?

Step 1: Add the digits together.
(4 + 7 + 1 + 5 + 4 + 4 + 8 + 7 + 3 + 5 + 4 + 4 + 8) = 64

Now check to see if the number 64 is divisible by 3. 64 is still a pretty large number. If you do not want to go through the long-division process of dividing 64 by 3, you can keep adding the digits together until you get a number that is easier to work with.

Step 2: Add the digits together.
(6 + 4) = 10

Step 3: Does 3 evenly divide into 10?
(10 /3) = 3 R 1

The answer is no. So 64 is not divisible by 3; therefore, 4,715,448,735,448 is not divisible by 3.

Divisible by 4: Check to see if the number formed by the last two digits of the original number is divisible by 4.

Example: Is the number 291,583,791,283 divisible by 4?

Step 1: Check to see if 83 (the last two digits of the original number) is divisible by 4.
(83 / 4) = 20 R 3
The answer is no. So 291,583,791,283 is not divisible by 4.

Divisible by 5: If the last digit is a 0 or 5, the number is divisible by 5.

Divisible by 5

Not Divisible by 5

5, 10, 1005, 80, 100

4, 13, 1007, 89, 101


Divisible by 6: If the number is divisible by both 2 and 3, then it is divisible by 6.

Example: Is the number 186 divisible by 6?

Step 1: Check to see if 186 is divisible by 2.
Since the last digit is a 6, 186 is divisible by 2.
Step 2: Check to see if 186 is divisible by 3.
(1 + 8 + 6) = 15
(15 / 3) = 5
Since 15 is divisible by 3, 186 is divisible by 3.
Therefore, since 186 is divisible by both 2 and 3, then 186 is also divisible by the number 6.
Divisible by 9: Add together all the digits; if the result is divisible by 9, then so is the original number.

Example: Is the number 78,957 divisible by 9?

Step 1: Add the digits together.
(7 + 8 + 9 + 5 + 7) = 36
Now check to see if the number 36 is divisible by 9.

Step 2: Add the digits together.
(3 + 6) = 9
Since 9 evenly divides into 9, (9 / 9 =1), 36 is divisible by 9. Therefore, 78,957 is divisible by 9.
Divisible by 10: If the number ends in a 0, then it is divisible by 10.

Example: Which number, 12345 or 123450, is divisible by 10?
The answer is 123450, because it ends in a 0. 12345 is not divisible by 10, because it ends in 5.

Math, Academics

  • Category:- Math
  • Reference No.:- M9542302

Have any Question?


Related Questions in Math

Questions -q1 prove the following identitiesa sinx y sinx

Questions - Q1. Prove the following identities a. sin(x + y) + sin(x - y) = 2 sin x cos y b. sec(x - y) = cos(x + y)/(cos 2 x - sin 2 y) c. tan 2 x - sin 2 x = (tan x sin x) 2 Q2. Solve the following equations for x ∈ [0 ...

Maths assignment - 1 analysis of a data setusing a

Maths Assignment - 1. Analysis of a data set Using a continuous data set you are requested to collect in the types of data and gathering data section, perform a statistical analysis on your data. You have opportunities t ...

Questions - provide solution to the following questionsq1

Questions - Provide solution to the following questions: Q1. Evaluate the following: ∫xsin3xdx Q2. If , then for what value of α is A an identity matrix? Q3. The line y = mx + 1 is a tangent to the curve y 2 = 4x. Find t ...

Assessment taskpractical investigation- question 1 requires

Assessment Task Practical Investigation - Question 1 requires selecting reference points from the graph. It is expected that each student will choose different reference points to other students. Take note of the criteri ...

1 suppose that n 10088821 is a product of two distinct

1. Suppose that n = 10088821 is a product of two distinct primes, and Φ(n) = 10082272. Determine the prime factors of n. 2. It is easy to show that the converse of Fermat's Theorem does not hold; i.e., the congruence a n ...

Assignment -question 1 let t and or 0 1 be a boolean

Assignment - Question 1. Let (T, ∧, ∨,', 0, 1) be a Boolean Algebra. Define ∗ : T × T → T and o : T × T → T as follows: x ∗ y := (x ∨ y)' x o y := (x ∧ y)' (a) Show, using the laws of Boolean Algebra, how to define x ∗ y ...

Assignment - provide solution to the following questionsq1

Assignment - Provide solution to the following questions: Q1. Evaluate the following: ∫xsin3x dx Q2. If , then for what value of α is A an identity matrix? Q3. The line y = mx + 1 is a tangent to the curve y 2 = 4x. Find ...

Question 1 what is the nth order approximation using taylor

Question: 1. What is the nth order approximation using Taylor series? 2. What is Error Propagation? 3. Please explain what the total numerical error is? Please illustrate how the change of step size will affect the total ...

Mathematics- algebraic geometry problemlet k denotes an

Mathematics- Algebraic Geometry Problem Let K denotes an algebraically closed field and let P 1 be constructed as in Example 5.5(a) in Gathmanns notes, i.e. P 1 is the gluing of X 1 = A 1 and X 2 = A 1 along  the open su ...

Mathematics- algebraic geometry problemlet k denotes an

Mathematics- Algebraic Geometry Problem Let K denotes an algebraically closed field and let P 1 be constructed as in Example 5.5(a) in Gathmanns notes, i.e. P 1 is the gluing of X 1 = A 1 and X 2 = A 1 along  the open su ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Why might a bank avoid the use of interest rate swaps even

Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate

Describe the difference between zero coupon bonds and

Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p

Compute the present value of an annuity of 880 per year

Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As

Compute the present value of an 1150 payment made in ten

Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int

Compute the present value of an annuity of 699 per year

Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As