Class 10 explanation of theorem 1.1
Answers
Answer:
*(Euclid's Division Lemma):
Step-by-step explanation:
Given positive integers a and b , there exist unique pair of integers q and r
satisfying a = bq + r , 0 < r < b .
Euclid's division algorithm is a technique to compute the Highest common factor (HCF) of two given integers . Recall that the HCF two positive integers a and b is the greatest positive integer d that divides both a and b.
Answer:
Theorem: Euclid's Division Lemma
Theorem of Euclid’s Division Lemma States that Given positive integers
a
and
b
, there exist unique integers
q
and
r
satisfying
a
=
b
q
+
r
,
0
≤
r
<
b
Euclid’s division algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers.
To obtain the HCF of two positive integers, say
c
and
d
, with
c
>
d
, steps given below is followed:
Step: 1. Apply Euclid’s division lemma, to
c
and
d
. So, we find whole numbers,
q
and
r
such that
c
=
d
q
+
r
,
0
≤
r
<
d
.
Step: 2. If
r
=
0
,
d
is the HCF of
c
and
d
. If
r
≠
0
, apply the division lemma to
d
and
r
.
Step: 3. Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.