find the HCF by prime factionsation method 10,25,80
Answers
Answer:
Here you will understand every steps
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Step-by-step explanation:
Here 25 is greater than 10
Now, consider the largest number as 'a' from the given number ie., 25 and 10 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b
Step 1: Since 25 > 10, we apply the division lemma to 25 and 10, to get
25 = 10 x 2 + 5
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 5 and 10, to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 10 and 25 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Here 80 is greater than 5
Now, consider the largest number as 'a' from the given number ie., 80 and 5 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b
Step 1: Since 80 > 5, we apply the division lemma to 80 and 5, to get
80 = 5 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 80 is 5
Notice that 5 = HCF(80,5) .
Therefore, HCF of 10,25,80 using Euclid's division lemma is 5.
SOLUTION
TO DETERMINE
The HCF by prime factorisation method 10 , 25 , 80
CONCEPT TO BE IMPLEMENTED
HCF :
For the given two or more numbers HCF is the greatest number that divides each of the numbers
EVALUATION
Here the given numbers are 10 , 25 , 80
We prime factorise the given numbers
10 = 2 × 5
25 = 5 × 5
80 = 2 × 2 × 2 × 2 × 5
Hence the required HCF
= The greatest number that divides each of the numbers
= 5
FINAL ANSWER
Hence the required HCF = 5
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