In this lesson, we will learn how to find the prime factors common to two or more numbers. To complete the objectives of this lesson, complete the following tasks:
- Study the lesson for mastery.
- Memorize the rule given in the lesson.
- Complete all lesson exercises.
- Complete the lesson assessment.
Lesson
To learn how to find the prime factors common to two or more numbers, let us begin with an example problem by which the rule may be understood.
1. What prime factors are common to 30 and 42?
Step 1. Write the numbers in line.
30 42
Step 2. From lesson 86, we know that 2 is a prime factor of both 30 and 42. Therefore, dividing both numbers by 2, the quotients are 15 and 21.
2 | 30 42
15 21
Step 3. We know that 3 is a prime factor of both quotients 15 and 21, and consequently of both 30 and 42. Dividing both numbers by 3, the quotients 5 and 7 are produced, which are prime to each other.
2 | 30 42
3 | 15 21
5 7
Solution: Therefore, 2 and 3 are the prime factors common to 30 and 42.
Rule for finding prime factors common to two or more numbers.
1. Write the given numbers in a line.
2. Divide by any prime number that will exactly divide all of them; divide the quotients in the same manner; and so continue to divide until two or more of the quotients are prime to each other.
3. The several divisors will be the common factors.
Exercises
Find the prime factors common to the following numbers:
- 60 and 90?
- 56 and 88?
- 72 and 84?
- 54 and 90?
- 81 and 108?
- 80 and 100?
- 84 and 126?
- 52, 68 and 76?
- 66, 78 and 102?
- 63, 99 and 117?
- 50, 70 and 110?
- 45, 75 and 105?
- 75, 125 and 175?
- 42, 70 and 98?
- 33, 55, 77 and 121?
- 39, 65, 91 and 104?
- 34, 51, 85 and 102?
- 38, 57, 95 and 114?
- 46, 69, 92 and 115?
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