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Find the H.C.F. of 45, 75, and 105.

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Question: Find the H.C.F. of 45, 75, and 105.

Options:

  1. 15
  2. 5
  3. 30
  4. 45

Correct Answer: 15

Solution: 

The H.C.F. of 45, 75, and 105 is 15.

Find the H.C.F. of 45, 75, and 105.

Practice Questions

Q1
Find the H.C.F. of 45, 75, and 105.
  1. 15
  2. 5
  3. 30
  4. 45

Questions & Step-by-Step Solutions

Find the H.C.F. of 45, 75, and 105.
  • Step 1: List the prime factors of each number.
  • Step 2: For 45, the prime factors are 3 x 3 x 5 (or 3^2 x 5).
  • Step 3: For 75, the prime factors are 3 x 5 x 5 (or 3 x 5^2).
  • Step 4: For 105, the prime factors are 3 x 5 x 7.
  • Step 5: Identify the common prime factors from all three numbers.
  • Step 6: The common prime factor is 3 and 5.
  • Step 7: Take the lowest power of each common prime factor.
  • Step 8: For 3, the lowest power is 3^1. For 5, the lowest power is 5^1.
  • Step 9: Multiply these together: 3^1 x 5^1 = 3 x 5 = 15.
  • Step 10: Therefore, the H.C.F. of 45, 75, and 105 is 15.
  • Highest Common Factor (H.C.F.) – The H.C.F. is the largest number that divides all the given numbers without leaving a remainder.
  • Prime Factorization – Finding the H.C.F. often involves breaking down each number into its prime factors.
  • Divisibility – Understanding which numbers can divide the given numbers is crucial for finding the H.C.F.
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