Find out the HCF of 8 and 12. Find out the HCF of 24 and 36. What is the HCF of 42, 52 ? What is the HCF of 24, 40? What is the HCF of 27, 45?
Answers
Answer:
The highest common factor (HCF) is found by finding all common factors of two numbers and selecting the largest one. For example, 8 and 12 have common factors of 1, 2 and 4. The highest common factor is 4.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 and 36. Therefore, common factor of 24 and 36 = 1, 2, 3, 4, 6, 8 and 12. Highest common factor (H.C.F) of 24 and 36 = 12.
Greatest common factor (GCF) of 42 and 52 is 2.
The highest common factor (HCF) of two numbers (or expressions) is the largest number (or expression) which is a factor of both. Consider the highest common factor of 24 and 40. The common factors of 24 and 40 are 2, 4, and 8. So, the highest common factor is 8.
The common factors of 27 and 45 are 9, 3, 1, intersecting the two sets above. In the intersection factors of 27 ∩ factors of 45 the greatest element is 9. Therefore, the greatest common factor of 27 and 45 is 9.
Given: Pairs of numbers
8 , 12
24 , 36
42 , 52
24 , 40
27 , 45
To Find: HCF
Solution:
HCF Highest common factor of given numbers is the largest factors which divides all the given numbers perfectly.
HCF = product of common factors of least power
8 , 12
8 = 2 * 2 * 2 = 2³
12 = 2 * 2 * 3 = 2² * 3¹
HCF = 2² = 4
Hence HCF ( 8 , 12) = 4
Similarly
HCF (24 , 36) = 12
HCF( 42 , 52) = 2
HCF (24 , 40) = 8
HCF (27 , 45) = 9
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