Question

Musa al-Khwarizini
50-850)
tCommon Factor
ositive integers a
uppose we need
integer, that is,
Example 1 : Use Euclid's algorithm to find the HCF of 4052 and 12576.
Solution :
Step 1 : Since 12576 > 4052, we apply the division lemma to 12576 and 4052, to get
12576= 40524 34420
Step 2 : Since the remainder 42060, we apply the division lemma to 4052 and 420, to
get
4052 = 420 x 9 + 272
Step 3: We consider the new divisor 420 and the new remainder 272, and apply the
division lemma to get
420= 272 x 1 + 148
We consider the new divisor 272 and the new remainder 148, and apply the division
lemma to get
272 = 148 x1 + 124
We consider the new divisor 148 and the new remainder 124, and apply the division
lemma to get
148 = 124 x 1 + 24
We consider the new divisor 124 and the new remainder 24, and apply the division
lemma to get
124 = 24 x 5+4
We consider the new divisor 24 and the new remainder 4, and apply the division
lemma to get
24 = 4 x 6 +0
vision lemma
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ny further
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work? It
The remainder has now become zero, so our procedure stops. Since the divisor at this
stage is 4, the HCF of 12576 and 4052 is 4.
Notice that 4 = HCF (24, 4) = HCF (124, 24) = HCF (148, 124) =
HCF (272, 148) = HCF (420, 272) = HCF (4052, 420) = HCF (12576, 4052).
Euclid's division algorithm is not only useful for calculating the HCF of very
large numbers, but also because it is one of the earliest examples of an algorithm that
a computer had been programmed to carry out.
follow how we do hcf​

Answer 1

Answer:

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