1. State Euclid division lemma.2. State Fundamental Theorem of Arithme

1.	1. State Euclid division lemma.2. State Fundamental Theorem of Arithmetic.
Answer» 1. For a pair of given positive integers ‘a’ and ‘b’, there exist unique integers ‘q’ and ‘r’ such thata=bq+r, where0≤r<bExplanation:Thus, for any pair of two positive integers a and b; the relationa=bq+r, where0≤r<bwill be true where q is some integer. 2. The fundamental theorem of arithmetic (FTA), also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is prime itself or is the product of a unique combination of prime numbers

1. State Euclid division lemma.2. State Fundamental Theorem of Arithmetic.

Answer»

1. For a pair of given positive integers ‘a’ and ‘b’, there exist unique integers ‘q’ and ‘r’ such thata=bq+r, where0≤r<bExplanation:Thus, for any pair of two positive integers a and b; the relationa=bq+r, where0≤r<bwill be true where q is some integer.

2. The fundamental theorem of arithmetic (FTA), also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is prime itself or is the product of a unique combination of prime numbers

Discussion

No Comment Found

Related InterviewSolutions

The bisector of an exterior angle at the vertex of an isosceles triangle isparallel to its base. State and prove its converse.
( x - 5 ) ( x - 6 ) = \frac 25 ( 24 ) ^ 2
Write any two rational numbers which are between 2.3 and 2.4.
3. State exterior angle property of a triangle
Mathematics for Class 7and name2. Given below are pairs of congruentriangles. State the property of congruencethe congruent triangles in each case.Q.50 50В 70.60 60
8D180 (linear pair property),Hence, AD bisects BC at right angles.EXERCISE 9(B). Given below are pairs of congruent triangles. State the property of congruence and name thecongruent triangles in each case
10. State the property illustrated in the following.-5 9 9,56 24 24X--=
3. Write two rational numbers between :NE(b)- and -COIN
mine the longest tape which can be used to measure exactly the lengths 7 m
Find the general solution of the equation: sin x + sin 3x + sin 5x-0.+ sin 3x sin 5x 0