Q3 of 114 Page 9

By what number should 1365 be divided to get 31 quotient and 32 as remainder?

By Euclid’s division lemma -


x = bq + r ….(1)


where q is the quotient,


r is the remainder


and b is the divisor.


According to the question, x = 1365, r = 32, q = 31, b = ?.


Putting the values in equation(1) -


∴ 1365 = b(31) + 32


⇒ 31b = 1333


⇒ b = 43


More from this chapter

All 114 →
1

What do you mean by Euclid’s division lemma?

 2

A number when divided by 61 gives 27 as quotient and 32 as remainder. Find the number.

 4

Using Euclid’s division algorithm, find the HCF of

i. 405 and 2520


ii. 504 and 1188


iii. 960 and 1575

 5

Show that every positive integer is either even or odd.