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Secondary 1 | Maths
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Date Posted: 4 years ago
Views: 352
Find the HCF OF 630 and 396.
630
= 2 x 315
= 2 x 3 x 105
= 2 x 3 x 3 x 35
= 2 x 3 x 3 x 5 x 7
= 2 x 3² x 5 x 7
396
= 2 x 198
= 2 x 2 x 99
= 2 x 2 x 3 x 33
= 2 x 2 x 3 x 3 x 11
= 2² x 3² x 11
As you can see from above,
2, 3² are common. So HCF = 2 x 3² = 18
So the largest possible length of a side of the square is 18cm.
ii)
396 ÷ 18 = 22
630 ÷ 18 = 35
So least number of squares
= 35 x 22
= 770
OR
Least number of squares
= Area of board ÷ area of 1 square
= (630 x 396) ÷ (18 x 18)
= 770
Largest possible length of a square
= 18cm
18 = 2 x 3 x 3
So the second largest possible length must be (3 x 3) since it's the next biggest factor of 18
(3 x 3)cm = 9cm
you can solve b ii) on your own
630
= 2 x 315
= 2 x 3 x 105
= 2 x 3 x 3 x 35
= 2 x 3 x 3 x 5 x 7
= 2 x 3² x 5 x 7
396
= 2 x 198
= 2 x 2 x 99
= 2 x 2 x 3 x 33
= 2 x 2 x 3 x 3 x 11
= 2² x 3² x 11
As you can see from above,
2, 3² are common. So HCF = 2 x 3² = 18
So the largest possible length of a side of the square is 18cm.
ii)
396 ÷ 18 = 22
630 ÷ 18 = 35
So least number of squares
= 35 x 22
= 770
OR
Least number of squares
= Area of board ÷ area of 1 square
= (630 x 396) ÷ (18 x 18)
= 770
Largest possible length of a square
= 18cm
18 = 2 x 3 x 3
So the second largest possible length must be (3 x 3) since it's the next biggest factor of 18
(3 x 3)cm = 9cm
you can solve b ii) on your own
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18cm
Date Posted:
4 years ago
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