Question

Karan has 180 blue marbles and 150 red marbles he went to pack them into packets containing marble of the same colour what is the maximum number of marble that each packet can hold​

Answer 1

The answer is 30 marbles.

Given,

Total number of blue marbles = 180

Total number of red marbles = 150

To Find,

The maximum number of marble that each packet can hold​ =?

Solution,

The maximum number of marble that each packet can hold​ is the HCF of 180 and 150. So, we will use  Euclid’s Lemma to find HCF of 180 and 150.

Step 1: Using  Euclid’s Lemma on 180 and 150

180 = 150*1 + 30

30 is not equal to 0. The remainder is not equal to 0

Step 2: Using  Euclid’s Lemma on 150 and 30

150 = 30*5 + 0

The remainder is equal to 0. Therefore, the process is stopped and HCF is the divisor in the last step.

HCF of 180 and 150 = 30

Hence, the maximum number of marble that each packet can hold​ is 30 marbles.

Answer 2

Answer:

The maximum number of marbles that each packet can contain is 30 marbles.

Given:

Total number of blue marbles = 180

Total number of red marbles =  150

To Find :

The maximum number of marbles that each packet contains ?

Solutions:

we will use Euclid's Lemma to find HCF OF 180 And  150.

Step 1 :

Using Euclid Lemma on both 180 and 150

180 = 150 × 1 +30

30 is not equal to 0 . The remainder is not equal to 0

Step 2:

150 = 30 × 5 +0

The remainder is equal to 0 .

∴ the process is stopped and the divisor of the last step is HCF

HCF of 180 & 150 = 30

Therefore, the maximum number of marble that each packet can hold = 30.

What is Euclid Lemma ?

If a prime p divides the product ab of two integers a and b , then p must divide at least one of those integers a or b. For example ---- if p= 19 , a=133 , b = 143 then ab = 133 × 143 = 19019, and since this is divisible by 19 , the lemma implies that one or both of 133 or 143 must be as well.

Learn more about Euclid Lemma :

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