Find the highest common factor (HCF) of 48 and 80.

Goal: Find the highest common factor (HCF) of 48 and 80.Step 1: Express both numbers as a product of their prime factors.To find the prime factors of 48, we can break it down:To find the prime factors of 80, we can break it down:Step 2: Determine the HCF from the prime factorisations.The HCF is the product of the common prime factors raised to the lowest power they appear in either factorisation.The prime factorisations are and .The only common prime factor is 2. The lowest power of 2 that is common to both is .Therefore, the HCF is:Conclusion: The highest common factor of 48 and 80 is 16.

Find the highest common factor (HCF) of 140 and 126.

Goal: Find the highest common factor (HCF) of 140 and 126.Step 1: We will use the prime factorisation method. First, we write each number as a product of its prime factors.The prime factorisation of 140 is:The prime factorisation of 126 is:To find the HCF, we identify the common prime factors and multiply them, using the lowest power of each common factor.The prime factorisations are and .The common prime factors are 2 and 7.The lowest power of 2 is .The lowest power of 7 is .The HCF is the product of these:Conclusion: The highest common factor of 140 and 126 is 14.

Find all the common factors of 8 and 12.

Goal: Find all the numbers that are factors of both 8 and 12.Step 1: List the factors of 8.The factors of a number are the whole numbers that divide into it without leaving a remainder.The factors of 8 are and .Step 2: List the factors of 12.Similarly, the factors of 12 are and .Step 3: Identify the common factors.We now look for the numbers that appear in both of the lists we created.Factors of 8: Factors of 12: The numbers that are in both lists are and . M1Conclusion: The common factors of 8 and 12 are 1, 2, and 4.

Find the largest odd number that is a common factor of 90 and 120.

Goal: Find the largest odd number that is a common factor of 90 and 120.Step 1: First, we find all the factors for each number.The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.Step 2: Identify the common factors from the two lists.The common factors of 90 and 120 are: 1, 2, 3, 5, 6, 10, 15, 30.Step 3: From the list of common factors, identify which ones are odd.The odd common factors are: 1, 3, 5, 15.Step 4: Find the largest number in the list of odd common factors.The largest number in the set is 15.Conclusion: The largest odd number that is a common factor of 90 and 120 is 15.

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IGCSE (CAMBRIDGE)|9th and 10th|Extended Maths (0580)

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