Integer is a thing complete in itself. Whole numbers are represented on the number line as shown here:
• If you move towards the right from the zero mark on the number line, the value of the numbers increases.
▪ If you move towards the left from the zero mark on the number line, the value of the numbers decreases.
i. Integers: The collection of the numbers, that is, … -3, -2, -1, 0, 1, 2, 3, …., is called integers.
ii. Negative integers: The numbers -1, -2, -3, -4… which are called negative numbers.
iii. Positive integers: The number 1, 2, 3, 4 …s, which are
• Euclid’s division lemma can be used to: a = b x q + r
• Find the highest common factor of any two positive integers and to show the common properties of numbers.
• Finding H.C.F using Euclid’s division lemma.
• Suppose, we have two positive integers ‘a’ and ‘b’ such that ‘a’ is greater than ‘b’. Apply Euclid’s division lemma to the given integers ‘a’ and ‘b’ to find two whole numbers ‘q’ and ‘r’ such that, ‘a’ is equal to ‘b’ multiplied by ‘q’ plus ‘r’.
• Check the value of ‘r’:
If ‘r’ is equal to zero then ‘b’ is the HCF of the given numbers. If ‘r’ is not equal to zero, apply Euclid’s division lemma to the new divisor ‘b’ and remainder ‘r’. Continue this process till the remainder ‘r’ becomes zero. The value of the divisor ‘b’ in that case is the HCF of the two given numbers.
• Square number:
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as 3 x 3. Some Important Points
- A number n is a prefer. square if n = m for some integer m
- A perfect square number is never negative
- A square number never ends in 2, 3, 7 or 8
- The number of zeros at the end of the perfect square is even.
- The square of an even number is odd and odd number is even.
- A perfect square number never leaves remainder 0 or “I on division by 3.
- If a number has a square root then its unit digit must be 0, 1, 4, 5, 6, or 9.