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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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