Question

1. Find the HCF of the following numbers using the
prime factorisation method.
(i) 612, 544
(ii) 225, 650
(iii) 450, 480
(iv) 272, 452
(v) 405, 890
(vi) 250, 470
(vii) 490, 540
(viii) 72, 140, 190
(ix) 140, 125, 320
(x) 144, 252, 630
​

Answer 1

$factors \: of \: 612 = 2 \times 2 \times 3 \times 3 \times 17 \\ \\ factors \: of \: 544 = 2 \times 2 \times \times 2 \times 2 \times 2 \times 17 \\ \\ hcf \: of \: 612 \: and \: 544 = 2 \times 2 \times 17 = 68$

$factors \: of \: 225 = 3 \times 3 \times 5 \times 5 \\ \\ factors \: of \: 650 = 2 \times 5 \times 5 \times 13 \\ \\ hcf \: of \: 225 \: and \: 650 = 5 \times 5 = 25$

$factors \: of \: 450 = 2 \times 3 \times 2 \times 3 \times 5 \times 5 \\ \\ factors \: of \: 480 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \\ \\ hcf \: of \: 450 \: and \: 480 = 2 \times 2 \times 3 \times 5 = 60$

$factors \: of \: 272 = 2 \times 2 \times 2 \times 2 \times 17 \\ \\ factors \: of \: 452 = 2 \times 2 \times 113 \\ \\ hcf \: of \: 272 \: and \: 452 = 2 \times 2 = 4$

$factors \: of \: 405 = 3 \times 3 \times 3 \times 3 \times 5 \\ \\ factors \: of \: 890 = 2 \times 5 \times 89 \\ \\ hcf \: of \: 405 \: and \: 890 = 5$

$factors \: of \: 250 = 2 \times 5 \times 5 \times 5 \\ \\ factors \: of \: 470 = 2 \times 5 \times 47 \\ \\ hcf \: of \: 250 \: and \: 470 = 2 \times 5 = 10$

$factors \: of \: 490 = 2 \times 5 \times 7 \times 7 \\ \\ factors \: of \: 540 = 2 \times 2 \times 3 \times 3 \times 3 \times 5 \\ \\ hcf \: of \: 490 \: and \: 540 = 2 \times 5 = 10$

$factors \: of \: 72 = 2 \times 2 \times 2 \times 3 \times 3 \\ \\ factors \: of \: 140 = 2 \times 2 \times 5 \times 7 \\ \\ factors \: of \: 190 = 2 \times 5 \times 19 \\ \\ hcf \: of \: 72 \: and \: 140 \: and \: 190 = 2$

$factors \: of \: 140 = 2 \times 2 \times 5 \times 7 \\ \\ factors \: of \: 125 = 5 \times 5 \times 5 \\ \\ factors \: of \: 320 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \\ \\ hcf \: of \: 140 \: and \: 125 \: and \: 320 = 5$

$factors \: of \: 144 = 2 \times 2 \times 2 \times 2 \times3 \times 3 \\ \\ factors \: of \: 252 = 2 \times 2 \times 3 \times 3 \times 7 \\ \\ factors \: of \: 630 = 2 \times 3 \times 3 \times 5 \times 7 \\ \\ hcf \: of \: 144 \: and \: 252 \: and \: 630 = 2 \times 3 = 6$

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