1. Use Euclid's algorithm to find the HCF of (i) 900 and 270 (ii) 196 and 3822 (iii) 1651 and 2032
2. Use division algorithm to show that any positive odd integer is of the form 6q+1, or 6q+3 or 6q+5,q is some integer.
3. Use division algorithm to show that the square of any positive integer is of the form 3p or 3p+1.
4. Use division algorithm to show that the cube of any positive integer is of the form 9m,9m+1 or 9m+8.
5. Show that one and only one out of n,n+2 or n+4 is divisible by 3,where n is any positive integer.
We know from Division Algoeithm thatvfor given positive integer a and b there exists unique pair of integers q and r satifying a=bq+r, 0≤r< b
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If r=0,then what is the relationship between a,b and q in a =bq+r? |
From the above discussion you might have concluded that if a =bq,"a" is divisible by "b"then we can say that "b" is a factor of "a".
For example we know that 24= 2×12
24 =8×3
=2×2×2×3
We know that,if 24= 2×12 then we can say that 2 and 12 ate factors of 24. We can also write 24=2×2×2×3 and you know that this is the prime factorisation of 24.