Question

How do you write the sum of the number 55 + 66 as the product of their GCF and another sum?

Answer 1

Hint: Now first we will find the factors of number 55 and 66. From the obtained factors we will find the GCF of the numbers. Then we will use distributive property to write the number in the form of GCF × (a + b). Where a and b are integers.

Complete step-by-step solution:
Now first consider the numbers 55 and 66.
Let us first factorize both the numbers into prime factors.
Factorization of 55 is 55 = 5 × 11. Since 5 and 11 are prime this is the prime factorization of 55.
Similarly 66 = 6 × 11 = 3 × 2 × 11. Since 3, 2, 11 are all prime this is the prime factorization of 66.
Now we can see that the common factors of 55 and 66 is 11.
Hence 11 is GCF of 55 and 66.
Now let us rewrite the expression 55 + 66 as 5 × 11 + 6 × 11.
Now we know that according to distributive property we have a × (b + c) = a × b + a × c.
Hence we can say that 5 × 11 + 6 × 11 = 11 × (5 + 6).
Hence 55 + 66 = 11 × (5 + 6).

Note: Note that GCF is the greatest common factor which is obtained by multiplying all the common factors of the given numbers. LCM is the least common multiple which is obtained by finding the common multiple of the two numbers. Hence not to be confused between the two. Always remember GCF will be less than or equal to the given numbers while LCM will be more than or equal to the given numbers.