# PROBLEMS ON NUMBERS

Problem 1 :

If a number when divided by 296 gives a remainder 75, find the remainder when 37 divides the same number.

Solution :

Let the number be ‘x’

Then x = 296k + 75, where ‘k’ is quotient when ‘x’ is divided by ‘296’

In the above sentence we have 296 is multiplied by the constant "k", 75 is added to that. In this form , we consider the number 75 as remainder when the number x is divided by 296.

We want to find the remainder when we divide the number "x" by 37. To do this, we need to have 37 at the place where we have 296 in the above equation.

So we can write 296 as 37 times 8 and 75 as 37 times 2 plus 1. It has shown below.

x  =  37  8k + 37  2 + 1

x = 37 ⋅ (8k + 2) + 1

So, the remainder is ‘1’ when the number ‘x’ is divided by 37.

Problem 2 :

Find the number of prime factors of

610 ⋅ 717  5527

Solution :

From 610  717  5527, we have to write each base in terms of multiplication of its prime factors.

That is,

=  (2 ⋅ 3)10  ⋅ (7)17 ⋅ (5 ⋅ 11)27

=  210 ⋅ 310 ⋅ 717 ⋅ 527 ⋅ 1127

The no. of prime factors  =  sum of the exponents

=  10 + 10 + 17 + 27 + 27

=  91

So, the number of prime factors is 91.

Problem 3 :

Find the unit digit of

24382643

Solution :

Step 1 :

Take the last two digits in the power and unit digit in the base. They are 43 and 2

Step 2 :

Divide the last two digits of the power by 4 (in all the problems) and get the remainder. That is, when 43 is divided by4, the remainder is 3.

Step 3 :

Now this remainder 3 has to be taken as exponent of the unit digit 2

That is, 23  =  8

So, the unit digit of the given number is 8.

Problem 4 :

Find the square root of 123454321

Solution :

In the given number, we have the first five natural numbers in ascending order up to 5.

After 5, we have the first four natural numbers in descending order.

Whenever we have a number like this and we want to find square root, we have to replace each digit by 1, up to the digit where we have the first n natural natural numbers in ascending order.

So, in our number 123454321, we have to replace each digit by 1 up to 5. That is the square root of 123454321.

So, the square root of 123454321 is 11111.

Problem 5 :

Find the least number which when divided by 35, leaves a remainder 25, when divided by 45, leaves a remainder 35 and when divided by 55, leaves a remainder 45.

Solution :

For each divisor and corresponding remainder, we have to find the difference.

35 - 25  =  10

45 - 35  =  10

55 - 45  =  10

we get the difference 10 (for all divisors and corresponding remainders)

Now we have to find the L.C.M of (35,45,55) and subtract the difference from the L.C.M.

L.C.M of (35,45,55)  =  3465

So, the required least number is

=  3465 - 10

=  3455 Apart from the stuff given above, iyou need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

1. Click on the HTML link code below.

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 