Question

An integer divisible by 2 is called \[\]
A. Even number\[\]
B. Odd number \[\]
C. Prime number \[\]
D. Composite number \[\]

Answer 1

Hint: We recall the dividend $ n $ , divisor $ d $ , quotient $ q $ , remainder $ r $ and the Euclid’s lemma $ n=dq+r $ . When have $ r=0 $ we say $ n $ is divisible by $ d $ . We recall even number as the numbers divisible by 2 and odd numbers as the numbers not divisible by 2. \[\]

Complete step by step answer:
We know that in the arithmetic operation of division the number we are going to divide is called the dividend, the number by which divides the dividend is called the divisor. We get a quotient which is the number of times the divisor is of dividend and also remainder obtained at the end of the division. If the number is $ n $, the divisor is $ d $, the quotient is $ q $ and the remainder is $ r $ , they are related by the following equation,
\[n=dq+r\]
Here the divisor can never be zero. The above relation is called Euclid’s Division Lemma. \[\]
If $ r=0 $ in $ n=dq+r $ then $ n $ is exactly divisible or divisible by $ d $ or $ n $ is a multiple of $ d $ . If we are going to divide natural numbers by 2 then we can get either remainder 0 and or we can remainder 1.\[\]
 If we get reminder 0 we say the number is divisible by 2 and the number is called odd numbers, for example, the even numbers are 2,4,6,8,10,.... and if we get remainder 1 we say the number is not divisible by 2 and the number is called the odd number, for example, the even numbers are 3,5,7,9,11,...
So an integer divisible by 2 is called an even number. Hence the correct option is A.\[\]

Note:
We note that the remainder is always less than the quotient that is $ r < q $ . So the possible remainders are $ 0,1,2,...,q-1 $ . If $ n $ is a multiple of $ d $ is factor of $ n $ . We note that if there are only 2 two factors (1 and the number itself) then the number is called prime otherwise composite. There is only one even prime number that is 2 and the rest primes are odd numbers.