Highest Common Factor (HCF) of two numbers is the greatest factor that is common to both of them
To find the greatest common divisor of the given numbers or for algebraic expressions we have to follow the steps.
Step 1 :
List the prime factors of each of the given number. For algebraic expression we have to find factors of them.
Step 2 :
List the common factors of the given numbers or common factors.
Step 3 :
Multiply those common factors.
Find the HCF of :
Example 1 :
4x and 12
Solution :
Factor of 4x and 12
4x = 2 ⋅ 2 ⋅ x
12 = 2 ⋅ 2 ⋅ 3
= 2 ⋅ 2
= 4
HCF of 4x and 12 is 4.
Example 2 :
3x and 6
Solution :
Factor of 3x and 6
3x = 3 ⋅ x
6 = 2 ⋅ 3
= 3
HCF of 3x and 6 is 3.
Example 3 :
3ab and 6b
Solution :
Factor of 3ab and 6b
3ab = 3 ⋅ a ⋅ b
6b = 2 ⋅ 3 ⋅ b
= 3b
HCF of 3ab and 6b is 3b.
Example 4 :
4y and 4xy
Solution :
Factor of 4y and 4xy
4y = 2 ⋅ 2 ⋅ y
4xy = 2 ⋅ 2 ⋅ x ⋅ y
= 2 ⋅ 2 ⋅ y
= 4y
HCF of 4y and 4xy is 4y.
Example 5 :
6x2 and 2x
Solution :
Factor of 6x2 and 2x
6x2 = 2 ⋅ 3 ⋅ x ⋅ x
2x = 2 ⋅ x
= 2x
HCF of 6x2 and 2x is 2x.
Example 6 :
3y and 9y2
Solution :
Factor of 3y and 9y2
3y = 3 ⋅ y
9y2 = 3 ⋅ 3 ⋅ y ⋅ y
= 3y
HCF of 3y and 9y2 is 3y.
Example 7 :
2(x – 1) and 3(x – 1)
Solution :
Factor of 2(x – 1) and 3(x – 1)
2(x – 1) = 2 ⋅ (x – 1)
3(x – 1) = 3 ⋅ (x – 1)
= (x – 1)
HCF of 2(x – 1) and 3(x – 1) is (x – 1).
Example 8 :
4(x + 2) and (x + 2)
Solution :
Factor of 4(x + 2) and (x + 2)
4(x + 2) = 2 ⋅ 2 ⋅ (x + 2)
x + 2 = (x + 2)
= x + 2
HCF of 4(x + 2) and x + 2 is (x + 2).
Example 9 :
3(x + 1) and (x + 1) (x – 4)
Solution :
Factor of 3(x + 1) and (x + 1) (x – 4)
3(x + 1) = 3 ⋅ (x + 1)
(x + 1) (x – 4) = (x + 1) ⋅ (x - 4)
= x + 1
HCF of 3(x + 1) and (x + 1) (x – 4) is (x + 1).
Example 10 :
(x - 2)2 and 2(x - 2) (x – 5)
Solution :
Factor of (x - 2)2 and 2(x - 2) (x – 5)
(x - 2)2 = (x - 2) ⋅ (x - 2)
2(x - 2) (x – 5) = 2 ⋅ (x – 2) ⋅ (x - 5)
= (x - 2)
HCF of (x - 2)2 and 2(x - 2) (x – 5) is (x - 2).
Example 11 :
2x(5 - x) and x2(5 - x)
Solution :
Factor of 2x(5 - x) and x2(5 - x)
2x(5 - x) = 2 ⋅ x ⋅ (5-x)
x2(5 - x) = x ⋅ x ⋅ (5-x)
= x . (5 – x)
= x(5 – x)
HCF of 2x(5 – x) and x2(5 - x) is x(5 – x).
Example 12 :
(x + 2)2 and 5(x - 4) (x + 2)
Solution :
Factor of (x + 2)2 and 5(x - 4) (x + 2)
(x + 2)2 = (x + 2) ⋅ (x + 2)
5(x - 4) (x + 2) = 5 ⋅ (x - 4) ⋅ (x + 2)
= (x + 2)
HCF of (x + 2)2 and 5(x - 4) (x + 2) is (x + 2).
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