Write the common factors of: (a) 25, 45 (b) 75, 125 (d) 100, 150 (e) 33, 55
The correct answer and explanation is:
Correct Answers:
(a) Common factors of 25 and 45:
1, 5
(b) Common factors of 75 and 125:
1, 5, 25
(d) Common factors of 100 and 150:
1, 2, 5, 10, 25, 50
(e) Common factors of 33 and 55:
1, 11
💡 300 Words Explanation:
To find the common factors of two numbers, we first list out all the factors (numbers that divide evenly into the given number) for each, and then identify the numbers that appear in both lists.
(a) 25 and 45
Factors of 25: 1, 5, 25
Factors of 45: 1, 3, 5, 9, 15, 45
Common factors: 1 and 5
(b) 75 and 125
Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 125: 1, 5, 25, 125
Common factors: 1, 5, 25
(d) 100 and 150
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Common factors: 1, 2, 5, 10, 25, 50
(e) 33 and 55
Factors of 33: 1, 3, 11, 33
Factors of 55: 1, 5, 11, 55
Common factors: 1 and 11
Why Common Factors Matter:
Common factors are used in many areas of math, including simplifying fractions, solving problems with ratios, and determining least common multiples or greatest common divisors (GCD). Knowing how to find them improves problem-solving and critical thinking skills in arithmetic and algebra. Identifying common factors can also help determine compatibility in grouping items, sharing resources, and optimizing processes in real-life applications.