Understanding Factors, Prime Numbers, and Divisibility Tests
This guide covers fundamental exercises on identifying factors, prime numbers, and checking divisibility. Learn how to list the factors of 64, determine which numbers from a set are prime, and apply divisibility tests for 2 and 6 on various integers. Additionally, explore practical applications of these concepts, such as arranging auditorium seats in equal rows. Develop a clear understanding of divisibility rules to enhance your mathematical skills.
Understanding Factors, Prime Numbers, and Divisibility Tests
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Presentation Transcript
Chapter 2 Section 2.1 Exercise #9
List the factors of the following number. 64 8 x 8 = 64 4 x 16 = 64 2 x 32 = 64 1 x 64 = 64 1, 2, 4, 8 , 16, 32, and 64 are all the factors of 64.
Chapter 2 Section 2.1 Exercise #13
Which of the given numbers are prime? 0, 1, 15, 19, 23, 31, 49, 55, 59, 87, 91, 97, 103, 105 55 0 59 1 87 15 91 19 97 23 103 31 49 105
Chapter 2 Section 2.1 Exercise #17
Which of the given numbers are divisible by 2? 45, 72, 158, 260, 378, 569, 570, 585, 3541, 4530, 8300 A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8. 45 570 72 585 158 3541 260 4530 378 8300 569
Chapter 2 Section 2.1 Exercise #19
Which of the given numbers are divisible by 6? 45, 72, 158, 260, 378, 569, 570, 585, 3541, 4530, 8300 A number is divisible by 6 if it is an even number and the sum of the digits is divisible by 3. 45 570 5 + 7 + 0 = 12 72 7 + 2 = 9 585 158 1 + 5 + 8 = 14 3541 260 2 + 6 + 0 = 8 4530 4 + 5 + 3 + 0 = 12 378 3 + 7 + 8 = 18 8300 8 + 3 + 0 + 0 = 11 569
Chapter 2 Section 2.1 Exercise #21
A school auditorium is to have 350 seats. The principal wants to arrange them in rows with the same number of seats in each row. Use the divisibility test to determine if it is possible to have rows of 10 seats each. Are 15 rows of seats possible? 350 is divisible by 10. 350 is not divisible by 15.
