Using Euclid's Division Algorithm, find the HCF of
(1). 4052 and 12576
(2). 870 and 225
(3). 441, 567 and 693
(4). 56, 96 and 404
Can you give the explanation or picture of answer
Answers
A.)Step 1: Since 12576 > 4052, apply the division lemma to 12576 and 4052, to get
12576 = 4052 × 3 + 420
Step 2: Since the remainder 420 ≠ 0, apply the division lemma to 4052 and 420, to get
4052 = 420 × 9 + 272
Step 3: Consider the new divisor 420 and the new remainder 272, and apply the division lemma to get
420 = 272 × 1 + 148
Consider the new divisor 272 and the new remainder 148, and apply the division lemma to get
272 = 148 × 1 + 124
Consider the new divisor 148 and the new remainder 124, and apply the division lemma to get
148 = 124 × 1 + 24
Consider the new divisor 124 and the new remainder 24, and apply the division lemma to get
124 = 24 × 5 + 4
Consider the new divisor 24 and the new remainder 4, and apply the division lemma to get
24 = 4 × 6 + 0
The remainder has now become zero, so procedure stops. Since the divisor at this stage is 4, the HCF of 12576 and 4052 is 4.
Also, 4 = HCF (24, 4) = HCF (124, 24) = HCF (148, 124) = HCF (272, 148) = HCF (420, 272) = HCF (4052, 420) = HCF (12576, 4052)
B) Step-by-step explanation:
Euclids division algorithm: If there are two positive integers a, b there exists q and r which satisfies a = bq + r where 0 < r ≤ b.
It is a technique used to find the highest common factor of two positive integers. HCF is the largest number that divides both the integers until the remainder is zero.
Out of the two given numbers, we consider the greater number first and then follow Euclids algorithm.
Now, here 870 is the greater number among the given numbers.
Hence, 15 is the HCF for 870 and 225.
3). By Euclid’s division algorithm, 693 = 567 x 1 + 126 567 = 126 x 4 + 63 126 = 63 x 2 + 0 So, HCF(441, 63) = 63 So, HCF (693, 567) = 63 441 = 63 x 7 + 0 Hence, HCF (693, 567, 441) = 63.
4).96=56×1+40
56=40×1+16
40=16×2+8
16=8×2+0
HCF=8
404=8×50+4
8=4×2+0
HCF(56,96,404)=4
May this helps uh
