Question

Sum of 2 numbers is 128 and their hcf is 8. how many numbers of pairs of numbers will satisfy this condition?

Answer 1

Answer:

Concept:

HCF refers for Highest Common Factor in its entire form. The HCF of two numbers is the highest factor that can evenly divide two numbers. HCF can be calculated using two or more numbers. It is the biggest divisor for any two integers that can divide them evenly or fully. The HCF, or Highest Common Factor, is the highest number that combines each of the two or more numbers. The Greatest Common Factor (HCF) is also known as the Greatest Common Measure (GCM) or the Greatest Common Divisor (GCD). HCM and LCM are two alternative ways for finding the smallest universal multiple of any two or more numbers. The Least Common Multiple (LCM) method is used to find the smallest common multiple of two or more integers.

Given:

The HCF of two numbers is 8 and their sum is 128.

Find:

find how many numbers of pairs of numbers will satisfy this condition?

Answer:

$HCF-8$ is the most prevalent factor among the values. So, let's say the first number is $=8x$ and the second number is $=8y$

then,

$8x+8y = 128\\x+y=16$

$(1,15), (3,13), (5,11)$  $and$  $(7,9)$ are the co-prime numbers that add up to 16 "Co-prime numbers are ones that share no common factor" These pairs were chosen because the highest common factor is used in HCF. As a result, there must be no common factors between the leftover multiples x and y. There are four pairs of co-prime numbers in this problem. There will be four pairs of numbers that meet the given criteria.

The dimensions are $(8*1,8*15),(8*3,8*13),(8*5,8*11),(8*7,8*9)$

Therefore, the answer is $4$

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Answer 2

Answer:

(8*1 , 8*`15) , (8*5 , 8*11) , (8*3, 8*13) , (8*7, 8*9)

i.e. ( 8 , 120) , (40 , 88) , ( 24 , 104) , ( 56 , 72) .

Step-by-step explanation:

Given :- Sum of two numbers is 128 . and their HCF is 8 .

To find :- The value of those two numbers .

Solution :-

Concept :-

• HCF is highest common factor , it is the greatest number which divides the two or more numbers .
• It is also called as greatest common divisor .
• HCF of prime number is always 1

Step 1) Let the first number = $8x$ , and second number = $8y$ . since the HCF is 8 .

Step 2) We have been given that the sum of the 2 numbers is 128,

$8x + 8y = 128 \\x+y = 16 .$

This tells us that the sum of the 2 numbers is 16 .

Step 3) Hence, now we will make the pair of those numbers which do not have any common factor , they are called as co-prime numbers .

They are , ( 1 , 15) , (5,11) , (3,13) , (7,9) , we have got 4 pair which satisfies the condition .

Answer :- (8*1 , 8*`15) , (8*5 , 8*11) , (8*3, 8*13) , (8*7, 8*9) .

i.e. ( 8 , 120) , (40 , 88) , ( 24 , 104) , ( 56 , 72) .

cross checking the answer ,

we know that the sum of the two numbers is 128 ,

therefore , if we take the first pair ( 8*1 , 8*15)

$x = 8*1 , y = 8*15 , \\x+y = 8 + (8*15) = 128 .$

similarly , we can go for other pairs , and verify the answer obtained .

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