This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the problems: 3. Find out whether the first number is a factor of the second number. a) 15, 225 Step 1: Divide the second number by the first number. (225)/(15) = 15 Since the remainder is 0, the first number is a factor of the second number. Answer: Yes b) 32, 800 Step 1: Divide the second number by the first number. (800)/(32) = 25 Since the remainder is 0, the first number is a factor of the second number. Answer: Yes c) 29, 581 Step 1: Divide the second number by the first number. (581)/(29) = 20 with a remainder of 21 Since the remainder is not 0, the first number is not a factor of the second number. Answer: No d) 42, 2772 Step 1: Divide the second number by the first number. (2772)/(42) = 66 Since the remainder is 0, the first number is a factor of the second number. Answer: Yes 4. Find the common factors of the following. a) 8 and 12 Step 1: List the factors of each number. Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 Step 2: Identify the common factors. Answer: 1, 2, 4 b) 24 and 36 Step 1: List the factors of each number. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Step 2: Identify the common factors. Answer: 1, 2, 3, 4, 6, 12 c) 8, 18 and 52 Step 1: List the factors of each number. Factors of 8: 1, 2, 4, 8 Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 52: 1, 2, 4, 13, 26, 52 Step 2: Identify the common factors. Answer: 1, 2 d) 9, 27 and 81 Step 1: List the factors of each number. Factors of 9: 1, 3, 9 Factors of 27: 1, 3, 9, 27 Factors of 81: 1, 3, 9, 27, 81 Step 2: Identify the common factors. Answer: 1, 3, 9 That's 2 down. 3 left today — send the next one.