Question

. Find common factors of the following numbers. Then find their H.C.F.
(a) 25, 45,
(b) 12, 28
(c) 16,56
(d) 44, 66
(e) 36, 60
(f) 56, 98
(g) 14,84
(h) 15, 80​

Answer 1

Answer:

(a) 25=5*5

45=3*3*5

common factor =5

Answer 2

$\red{a) \: 25 , 45 }$

$Common \: factors \: of \: 25 = \{ 1,5,25\}$

$Common \:factors \:of \: 45$

$= \{ 1,3,5,9,15,45\}$

$25 = 5 \times 5 = 5^{2}$

$45 = 3 \times 3 \times 5 = 3^{2} \times 5$

$\green{HCF (25,45) = 5}$

$\blue{ ( Product \:of \:the\: smallest \:power}$

$\blue{of \:each\:common \:prime\:factors}$

$\blue{ of \:the \: numbers )}$

$\red{ b) 12 , \:28 }$

$Common \: factors \: of \: 12 = \{ 1,2,3,4,6,12\}$

$Common \:factors \:of \: 28$

$= \{ 1,2,4,7,14,28\}$

$12 = 2\times 2 \times 3= 2^{2} \times 3$

$28 = 2\times 2 \times 7= 2^{2} \times 7$

$\green{ HCF(12,28) = 2^{2} = 4 }$

$\red{ c) 16 , \:56 }$

$Common \: factors \: of \: 16 = \{ 1,2,4,8,16\}$

$Common \:factors \:of \: 56$

$= \{ 1,2,4,7,8,14,28,56\}$

$16 = 2\times 2 \times 2\times 2= 2^{4}$

$56 = 2\times 2 \times 2 \times 7= 2^{3} \times 7$

$\green{ HCF(16,56) = 2^{3} = 8 }$

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