Question

Find the hcf of 12576 and 4052 by using the prime factorization method

Answer 1

Hey

Here is your answer,

By division algorithm :

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)x

Prime factorisation :

The prime factors for 12576 = 2 * 2 * 2 * 2 * 2 * 3 * 131
The prime factors for 4052 = 2 * 2 * 1013

Hcf = 4

Hope it helps you!

Answer 2

Step-by-step explanation:

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