Question
The highest common factor (HCF) of 60 and 144 is equal to:
Ask by Clarke Hill. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The highest common factor of 60 and 144 is 12.
Solution
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Prime Factorization of 60:
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Prime Factorization of 144:
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Determine the HCF:
The HCF is found by taking the product of the lowest powers of all prime factors common to both numbers. The common prime factors areand . - For
: take (since has and has ) - For
: take (since has and has )
Thus, the HCF is: - For
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Final Answer:The highest common factor of 60 and 144 is
.
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Simplify this solution The Deep Dive
The highest common factor (HCF) of 60 and 144 can be found by breaking down both numbers into their prime factors. For 60, the primes are 2 x 2 x 3 x 5 (or 2² x 3¹ x 5¹), and for 144, the primes are 2 x 2 x 2 x 2 x 3 x 3 (or 2⁴ x 3²). The common prime factors are 2 and 3, and their lowest powers are 2¹ and 3¹. Thus, HCF = 2¹ x 3¹ = 6.
To better understand the HCF, think of it as the largest “party size” you could organize with groups of 60 and 144 people, where each group is as large as possible without leaving anyone out. You’d organize them into groups of 6! This party planning analogy helps visualize the concept of common factors and sharing resources.
