Face Value:
The face value of a digit in a numeral is its own value, at whatever
place it may be. eg. in 6872 the face value of 7 is 7.
Place Value:
The Place value of a digit in a numeral is its value as per position, at
whatever place it may be. eg. in 6872 the Place value of 7 is 70.
Natural Numbers:Counting
no. are called natural numbers. eg. 1, 2, 3, 4, .......
Whole Numbers:
All counting no. including zero are called Whole numbers. eg. 0, 1, 2, 3, 4,
.......
Integers:
All counting numbers, zero and negative numbers are called integers. eg. ...,
-3, -2, -1, 0, 1, 2, 3, .....
Even Numbers:
All numbers divisible by 2 are called even no. eg. 2, 4, 6, .....
Odd Numbers:
All numbers not divisible by 2 are called odd no. eg. 1, 3, 5, .....
Prime Number: A
no which is divisible by 1 or itself is called Prime number. eg. 2, 3, 5, 7,
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53....
Co-Prime:
Two natural no are said to be co-prime if their HCF is 1. eg. (2, 3), (7, 9),
(23,24), etc
Divisibility:
Divisibility by 2: A
no is divisibile by 2 if its unit digit is 0, 2, 4, 6, 8. eg. 58888
Divisibility by 3: A
no is divisible by 3 if the sum of all its numeral is divisible by 3. eg.
111111 total is 6 which is multiple of 3.
Divisibility by 4: A
no is divisible by 4 if its last two numerals are divisible by 4. eg. 111116,
here 16 is divisible by4.
Divisibility by 5: A
no is divisible by 5 if its unit digit is 0 or 5. eg. 22225 or 11110.
Divisibility by 6: A
no is divisible by 6 if it is divisible by 2 and 3.
Divisibility by 8: A
no is divisible by 8 if its last three no are divisible by 8. 123123352 .
Divisiblity by 9: A
no is divisible by 9 if the sum of its numerals is divisible by 9. eg 111111111
here total of numerals is 9 so it is divisible by 9.
Divisibility by 10:
A no is divisible by 10 if its unit digit is zero. eg 1230.
Divisibility by 11:
A no is divisible by 11 if the difference between the sum of its digits at odd
places and the sum of digits at even places is either 0 or a no divisible by
11. eg. 29435417. now (7+4+3+9)-(1+5+4+2)=11 which is divisible by 11.
EXERCISE
1. The difference between the place value and the face
value of 6 in the numeral 856973 is :
a. 973 b. 6973 c. 5994 d. None
2. The unit digit in (784 x 618 x 917 x 463 )
is: a. 2 b. 3 c. 4 d.
5,
3. If the no 481*673 is fully divisible by
9, than smallest whole no in place of * is: a. 2 b. 5 c. 6 d. 7 e. None
4. If the no 97215*6 is fully divisible by
11, than smallest whole no in place of * is: a. 3 b. 2 c. 1 d. 5. e.
None
5 Which one of the following no is
completely divisible by 45: a. 181560 b. 331145 c. 202860 d. 1033550 e.
None.
6. The smallest prime no is:
a. 0 b. 1 c. 2 d. 3 e. None
7. Which one of the following cannot be square
of a natural no.: a. 32761 b. 81225 c. 42437 d. 20164 e. None
8. Which one of the following is divisible by
11 : a. 235641 b. 245642 c. 315624 d. 415624 e. None
Topic
1 ANSWER: 1 C, 2 A, 3 D, 4 A, 5
C, 6 C, 7 C, 8 D
tags : numbers, square, divisibility,digits
