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 Topic: divisibility
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Divisibility by 3 2018-11-20
From Ray:
There is a rule that a number is divisible by 3 if the sum of its digits are divisible by 3 (for example, 81=8+1=9 {divisible by 3} and 33=3+3=6 {again, divisible by 3}) I know this works but I don't know why! Please help.
27000001 2017-10-09
From Tulashiram:
If a× b =27000001, then what is the value of a & b ?
How many guests were present? 2017-09-17
From SM:
How many guests were present at an Italian dinner if every 2 guests shared a bowl of salad, every 3 guests shared a bowl of pasta, and every four guests shared a bowl of meatballs, and there were 65 bowls used altogether?
Is a large integer divisible by 2^n? 2017-03-28
From Sahand:
You are given number x that is very large (that large that it can't be divided by hand) can we find out that x is divisible by 2^n or not?
Divisibility of 3n^5+7n 2016-12-14
From Parag:

Question from Parag, a student:

if n is a natural number,then 3n^5+7n is divisible by
a)2
b)3
c)5
d)7

i got the answer but still i need a valid alternate approach.

How many boats total are in the marina? 2015-04-15
From Carla:
In a marina, 3/4 of the boats are white, of the remainder 4/7 are blue, the rest are red. There are 9 red boats. How many boats total are in the marina? My answer is 84 because if 1/4 of the boats are divided into sevenths, that makes the whole marina a 28 part item. 3/28 are red so 84 is the total number of boats. My child thinks I am wrong.
4821x14y is an 8-digit number divisible by 72 2014-08-06
From RAYA:
if 4821x14y is an 8-digit number divisible by 72. How many values can x and y take?
A 4 digit number 2014-04-04
From LIM:
"A" is a 4 digit number formed by all the numbers from 1 to 4. When "A" is divided by 9, the remainder is the biggest possible value. What is the biggest value of A?
A 2-digit number 2013-05-13
From A teacher:
Find a “2-digit number” where the sum of the 1st digit (on the Left) and the square of the 2nd digit equal the same number.
Answered by Lorraine Dame, Harley Weston.
Some 6 digit numbers 2012-10-23
From Mason:
How many different 6 digit numbers can you make using the digits 1 ,2 5, 6, 7, and 9? How many of these six-digit numbers are divisible by 6?
Squares and triangles 2011-12-06
From Liaqath:
You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have?

An even multiple of 27 2011-02-01
From parth:
the 6 digit # 63x904 is an even multiple of 27 what is X
Powers 2010-10-20
From dylan:
how do you write 20736 in exponential form .same for 1728 and 50625.

is there a formula to figure out how to express large know numbers in exponential form.

(x^3 + 11x) is divisible by 6 2010-06-24
From PT:
Given that x is a non-zero integer, how do you show that for all values of x, (x3 + 11x) is divisible by 6?

I know it works but how do I answer the "all values of x" part?

Divisibility by 3 2010-05-23
From Cathleen:
To math central. I have to do a maths extension question that I don't understand. At first I thought I did. It is about the dividing by three. In one part of the question, it asks me to show that the rule of division by three does not work for 23142 with a little 5 down the bottom. What doe base 5 mean? We first thought that the little 5 down the bottom meant multiplying y the power of five. Can you please tell me what it means so I can finish this question?
The difference of the two numbers 2010-02-15
From Steve:
The difference of the two numbers 'abcdef ' and ' fdebca ' is divisible by 271. prove that b = d and c = e.
Two questions from math class 2009-06-18
From Con:
Hello,

My name is Con and my son is required to answer the following questions for his maths class.

He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct?

He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution?

Q1.
Digits 2, 3, 4, 5 and 7 are each used once to compose a 5-digit number abcde such that 4 divides a 3-digit number abc, 5 divides a 3-digit number bcd and 3 divides a 3-digit number cde. Find the 5-digit number abcde.

Q2.
Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD. Con

Divisibility 2009-06-17
From Sophia:
Hello

a) Determine the remainder when 2^2009 + 1 is divided by 17;
b) Prove that 30^99 + 61^100 is divisible by 31;
c) It is known that numbers p and 8p^2+1 are primes. Find p.

Again, your assistance is greatly appreciated.
Thanks
Sophia

Divisibility by 11 2008-07-04
From Peter:
For what single digit value of n is the number n53nn672 divisible by 11?
The smallest number divisible by 1 to 9 2008-06-26
From Peggy:
What is the smallest number divisible by each of the first nine counting numbers?
The sum of the digits of a number 2008-06-23
From Ben:
Question: Using mathematical induction, prove that if the sum of the digits of a number is divisible by three, then the number itself is also divisible by 3.
Nine digit numbers 2008-05-21
From Alex:
List of Nine digit numbers, that can be divided by nine?
I am a 4-digit number 2008-02-12
From Nickie:
I am a 4-digit number with no repeating digits. I am divisible by 5, my first two digits (left to right) make a number divisible by 3, and my first three digits make a number divisible by 4. Also, my digits have a sum of 19 and I have the digit 7 in the thousands place. Who am I?
How many combinations of 8614 are divisible by 7? 2008-01-22
From Rebecca:
How many combinations of 8614 are divisible by 7 equally (with no remainder)?
Divisibility 2007-05-18
From Ashish:
A number is divisible by 2^n if the last n digits of the number are divisible by 2^n. Why?
Answered by Penny Nom and Claude Tardif.
Divisibility by 9 and 11 2006-10-04
From Prakai:
can 818991 divisible by 9, or 11?
Divisibility by each of the first ten counting numbers 2005-10-17
From Simon:
determine smallest positive integer that is divisible by each of the first ten counting numbers
Divisibility of a^2 + b^2 2005-05-16
From Ampa:
given natural numbers a and b such that a2+b2 is divisible by 21, prove that the same sum of squares is also divisible by 441.
Divisibility by 15 2004-12-19
From Lisa:
My son was asked to find divisiblity rules for 15. We have been unable to find the answer. Does it exist?
Answered by Leeanne Boehm and Denis Hanson.
Divisibility by 7 and 11 2004-10-13
From Tammy:
I'm stuck in class in Yr 7 And I'm finding it hard on our new topic Divisibility! When I try to find out what this means on Internet sites i can not understand the used symbols like algebra and so on. I'm stuck on the divisibility rules for the number 11!
Divisibility by 7 2003-11-14
From A student:
how do you test a number to see if it is divisible by 7 or not?
Divisibility by 2 or 5 or both 2003-10-30
From Abdu:
How many positive integers less than 1,001 are divisible by either 2 or 5 or both?
39 consecutive natural numbers 2003-08-19
From A student:
Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11.
The cousin of Sally's sister's boyfriend 2003-01-23
From Michael:
Sally went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Sally cannot carry more than 2.5kg, and that the eggs were raw, calculate how many eggs the cousin of Sally's sister's boyfriend received.
abc,abc 2002-11-20
From Pam:
Prove or disprove that "every number of the form abc,abc (where a, b, and c represent digits) is divisible by 7,11, and 13"
Two problems 2002-10-14
From Eva:

a) How many different equivalence relations can be defined on the set X={a,b,c,d}?

b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof.

Answered by Leeanne Boehm and Penny Nom.
Divisibility of 5 2002 2002-08-25
From Simon:
I need to ask you a question if 5 2002 and 3 2002 are divisible by 26.
Nickles, dimes, quarters and fifty cent pieces 2002-01-08
From A parent:
The total for all coins counted is \$4,564.50 The last coin added to the pile is a 50 cent piece There are 8 times as many 50 cent pieces as there are quarters There are 6 times as many dimes as nickles How many of each are there?
Divisibility rules 2001-09-07
From A student:
Why is it that when you add the digits of a number you can tell what the multiples of that number are. Example: 12131313111,

1+2+1+2+1+3+1+1+1=18,

therefore 12131313111 is divisble by 2, 9, 18, & 3 because those numbers are divisble by 18.

Divisibility by 16 2000-12-12
From Shiling:
A number can be divided by 16 if and only if its 1st four digits can be divided by 16. How can you prove that?
Divisibility by 9 2000-10-24
From Kelera:
If the sum of the digits of a number is divisible by 9, then the number itself it divisible by 9. Why is that? How do you explain this?
Divisibility by 3 2000-03-24
From Pat Walsh:
W hy does it work when you add the digits of a number then divid by three to see if the number is divisible by three
Six digit numbers using 1,2,5,6,7, and 9 2000-03-20
From Rachel:
How many different six-digit numbers can you make using the digits 1,2,5,6,7, and 9? How many of these six digit numbers are divisible by six?
Answered by Claude Tardif and Denis Hanson.
111...1222...2 1999-08-11
Let N = 111...1222...2, where there are 1999 digits of 1 followed by 1999 digits of 2.
Express N as the product of four integers, each of them greater than 1.

Divisibility by 9 1999-02-21
From Razzi:
I've been having a hard time trying to solve the following problem and I was wondering if you could help me.

For any positive integer a let S(a) be the sum of its digits. Prove that a is divisible by 9 if and only if there exist a positive integer b such that S(a)=S(b)=S(a+b).
Answered by Chris Fisher and Harley Weston.

Divisibility by 11 1998-10-28
From Pat Duggleby:
I am an upgrading instructor at a drop-in program in Regina. One of my students is taking General Math 30 through correspondence, and we have run into some confusing instructions. The section is about divisibility rules, and we did just fine up until the rule for Divisibility by 11. The statement is as follows:
 If the difference between the sum of the odd-numbered digits and the sum of the even-numbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11.
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