Question

3. Find the HCF by prime factorisation method :
(i) 138, 375
(ii) 170, 405 (iii) 144, 576, 804 (iv
Find het mbo 1:​

Answer 1

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Answer 2

HCF by Prime Factorisation

(i) 138, 375

Solution:

• 138 = 2 × 69
• = 2 × 3 × 23
• 375 = 3 × 125
• = 3 × 5 × 25
• = 3 × 5 × 5 × 5
• Thus HCF = 3, since 3 is the only common term in the above factorisations.

(ii) 170, 405

Solution:

• 170 = 2 × 85
• = 2 × 5 × 17
• 405 = 3 × 135
• = 3 × 3 × 45
• = 3 × 3 × 3 × 15
• = 3 × 3 × 3 × 3 × 5
• Thus HCF = 5, since 5 is the only common term in the above factorisations.

(iii) 144, 576, 804

Solution:

• 144 = 2 × 72
• = 2 × 2 × 36
• = 2 × 2 × 2 × 18
• = 2 × 2 × 2 × 2 × 9
• = 2 × 2 × 2 × 2 × 3 × 3
• 576 = 2 × 288
• = 2 × 2 × 144
• = 2 × 2 × 2 × 72
• = 2 × 2 × 2 × 2 × 36
• = 2 × 2 × 2 × 2 × 2 × 18
• = 2 × 2 × 2 × 2 × 2 × 2 × 9
• = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
• 804 = 2 × 402
• = 2 × 2 × 201
• = 2 × 2 × 3 × 67
• Thus HCF = 2 × 2 × 3, since these are the only common terms in the above factorisations
• = 12.