Number systems

Number Systems

It’s all about 0 & 1 & both has its importance. Again number system is one of the topics which needs more practice so that you can get exposed to a lot of new patterns. This section requires time to prepare. We are sharing few tricks along with a link to refer to.

 If you have to find the square of numbers ending with ‘5′.
Example1. 25 * 25. Find the square of the units digit (which is 5) = 25. Write this down. Then take the tenths digit (2 in this case) and increment it by 1 (therefore, 2 becomes 3). Now multiply 2 with 3 = 6. Write ‘6′ before 25 and you get the answer = 625.

Example 2. 45 * 45. The square of the units digit = 25
Increment 4 by 1. It will give you ‘5′. Now multiply 4 * 5 = 20. Write 20 before 25. The answer is 2025.

Example 3. 125*125.
The square of the units digit = 25. Increment 12 by 1. It will give you 13. Now multiply 12*13 = 156. Write 156 before 25. The answer is 15625.

HCF & LCM:

Highest Common Factor (H.C.F.) or Greatest Common Measure (G.C.M.) or Greatest Common Divisor (G.C.D.)
The Highest Common Factor H.C.F. of two or more than two numbers is the greatest number that divided each of them exactly.

There are two methods of finding the H.C.F. of a given set of numbers:
I. Factorization Method: Express the each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.

II. Division Method: Suppose we have to find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is required H.C.F.

Finding the H.C.F. of more than two numbers: Suppose we have to find the H.C.F. of three numbers, then, H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given number.
Similarly, the H.C.F. of more than three numbers may be obtained.
Least Common Multiple (L.C.M.):
The least number which is exactly divisible by each one of the given numbers is called their L.C.M.
There are two methods of finding the L.C.M. of a given set of numbers:

III. Factorization Method: Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.
IV. Division Method (short-cut): Arrange the given numbers in a row in any order. Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.
2. Product of two numbers = Product of their H.C.F. and L.C.M.
3. Co-primes: Two numbers are said to be co-primes if their H.C.F. is 1.