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Real Numbers

Question
CBSEENMA10006250
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What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively.

Solution

Clearly the required number is the HCF of the following numbers

626 - 1 = 625, 3127 - 2 = 3125 and

15628 - 3 = 15625

Case I. Finding the HCF of 625 and 3125 by applying Euclid’s division lemma.

I. 3125 = 625 × 5 + 0

Since, the remainder at this stage is zero, so the divisor i.e., 625 at this stage is the HCF of 625 and 3125.
Case II. Finding the HCF of 625 and third number 15625 by applying Euclid’s division lemma.


Now, the remainder at this stage is zero. So the divisor i.e., 625 at this stage is the HCF of 625 and 15625.

Hence, HCF of (626, 3127, 15628) is 625.

Some More Questions From Real Numbers Chapter

Use Euclid’s division algorithm to find the HCF of:

(i)135 and 225 (ii) 196 and 38220.

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Express each number as a product of its prime factors: (i) 140 

Express each number as a product of its prime factors: (ii) 156 

Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Express each number as a product of its prime factors: (iv) 5005 

Express each number as a product of its prime factors:  (v) 7429

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