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Maths:Number System Concepts:

Maths:Number System Concepts:

1.
43/7
7 =>divisor
43 =>dividend
6 =>Quotient
1 =>Remainder


2.
Factors
42 = 7*2*3
Here 7,2 and 3 are factors of 42.
42 is a multiple of 6.
42 is a multiple of 7.

If a, b are integers(b is not 0)and a/b is an integer.
=> b is a factor of a.
=>a is divisible by b.
=>a is a mulitple of b.
E.g. Positive factors of 12 = 1,2,3,4,6,12.
E.g. Multiples of 12 = 12,24,36,0, -12,-36.......

3.
To find total number of factors.
180= 2^2 *3^2 *5
=>(2+1)*(2+1)*(1+1)=18
=>18*2= 36 ;to include negative factors


4.
Always consider intensive counting unless mentioned otherwise.

5.
Never forget to check negative numbers.

6.
Numbers with exactly three divisors:
Squares of prime numbers.
E.g. => 49,121
They have exactly three factors : 1,7,49 & 1,11,121.

7.
Numbers with exactly 4 divisors:
product of two prime numbers.
E.g.=>21
They have exactly four factors : 1,3,7,21.

8.
Zero is neither positive nor negative.

9.
All integers except zero are factors of zero and zero is multiple of every integer.

10.
Divisibility rules for:
Last digit must be divisible by 2.
Sum of digits must be divisible by 3.
Number formed by last two digits must be divisible by 4.
Last digit must be 0 or 5.
Number must be divisible by both 2 and 3.

11.
In the number 456.789
4 is the Hundred's digit
5 is the Ten's digit
6 is the Unit's digit
7 is the Tenth's digit
8 is the Hundredth's digit
3444.782 rounded to nearest tenth's will be 3444.8
3444.749 rounded to nearest tenth's will be 3444.7

12.
Comparison of fractions:
By Cross multiplication:
compare 6/11 OR 5/9
compare 6*9 OR 11*5
compare 54 OR 55
R.H.S is greater so, 5/9 > 6/11.

General rules for fraction comparison.

If numerator increases, and denomitor remains same, then ratio increases.
=> 6/21 > 3/21
If denominator increases, and numerator remains same, then ratio decreases.
=> 6/21 > 6/22
If a constant is multiplied to both numerator and denominator, then ratio remains same.
=> 2/5 = 6/30 = 12/60