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The sum of two numbers is 58 and the product of them is 357. The HCF of the numbers is..
- A17
- B1
- C7
- D3
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CCommunity
Let assume one of the number as x and other as y,
x + y = 58 ----(I)
x × y = 357
⇒ x = 357/y ----(II)
Substitute the value of Eq(II) in Eq(I)
⇒ 357/y + y = 58
⇒ 357 + y2 = 58y
⇒ y2 – 58y + 357 = 0
⇒ y2 – 51y – 7y + 357 = 0
⇒ y(y – 51) – 7(y – 51) = 0
⇒ (y – 7) (y – 51) = 0
Let consider y = 7,
Value of x = 357/7 = 51
Factors of 7 = 7
Factors of 51 = 17 × 3 = 3, 17
∴ HCF (7, 51) = 1
x + y = 58 ----(I)
x × y = 357
⇒ x = 357/y ----(II)
Substitute the value of Eq(II) in Eq(I)
⇒ 357/y + y = 58
⇒ 357 + y2 = 58y
⇒ y2 – 58y + 357 = 0
⇒ y2 – 51y – 7y + 357 = 0
⇒ y(y – 51) – 7(y – 51) = 0
⇒ (y – 7) (y – 51) = 0
Let consider y = 7,
Value of x = 357/7 = 51
Factors of 7 = 7
Factors of 51 = 17 × 3 = 3, 17
∴ HCF (7, 51) = 1