The sum of any two even numbers is always an even number.

Let's denote two even numbers as 2n2n and 2m2m, where nn and mm are integers.

The sum of these two even numbers is: 2n+2m=2(n+m)2n+2m=2(n+m)

Since nn and mm are integers, n+mn+m is also an integer. Therefore, the sum 2(n+m)2(n+m) is an even number because it is divisible by 22. Thus, the sum of any two even numbers is an even number.

To find the product of two numbers given their least common multiple (LCM) and highest common factor (HCF), you can use the relationship between the product, LCM, and HCF of two numbers.

Let the two numbers be xx and yy.

Given:

1. LCM of xx and yy = 15
2. HCF of xx and yy = 4

We know that the product of two numbers is equal to the product of their LCM and HCF. That is:

x×y=LCM(x,y)×HCF(x,y)x×y=LCM(x,y)×HCF(x,y)

Substitute the given values:

x×y=15×4x×y=15×4

x×y=60x×y=60

So, the product of the two numbers is 6060.

To find the highest common factor (HCF) of two numbers, we find the largest number that divides both of them without leaving a remainder.

For the numbers 5 and 7, the only common factor they share is 1, since both 5 and 7 are prime numbers. Since there are no other common factors besides 1, the HCF of 5 and 7 is 1.

To find the factors of a number, you need to identify all the numbers that divide the given number evenly, including 1 and the number itself.

Let's find the factors for each:

(a) Factors of 12: 1, 2, 3, 4, 6, 12

(b) Factors of 18: 1, 2, 3, 6, 9, 18

These are all the possible factors of 12 and 18.