Podcast
Questions and Answers
Match the following factors of 5 in the product 15 × 16 × 17 × 18 × 20 × 21 × 24 × 25 × 27 × 28 with their corresponding number of factors of 5:
Match the following factors of 5 in the product 15 × 16 × 17 × 18 × 20 × 21 × 24 × 25 × 27 × 28 with their corresponding number of factors of 5:
15 = 1 20 = 1 25 = 2 18 = 0
Match the prime factors in the product 15 × 16 × 17 × 18 × 20 × 21 × 24 × 25 × 27 × 28 with their corresponding power in the product:
Match the prime factors in the product 15 × 16 × 17 × 18 × 20 × 21 × 24 × 25 × 27 × 28 with their corresponding power in the product:
3 = 4 2 = 12 5 = 4 7 = 2
Match the following numbers with their number of factors of 2:
Match the following numbers with their number of factors of 2:
16 = 4 20 = 2 24 = 3 28 = 2
Match the following concepts related to counting trailing zeros in a product with their definitions:
Match the following concepts related to counting trailing zeros in a product with their definitions:
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Match the following steps in calculating the number of trailing zeros in a product with their corresponding description:
Match the following steps in calculating the number of trailing zeros in a product with their corresponding description:
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Flashcards
Trailing Zeros
Trailing Zeros
The number of zeros at the end of a product.
Factors of 10
Factors of 10
10 is composed of 2 and 5 as factors.
Counting Factors of 5
Counting Factors of 5
Identify how many times 5 is a factor in the product.
Counting Factors of 2
Counting Factors of 2
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Determining Trailing Zeros
Determining Trailing Zeros
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Study Notes
Counting Zeros in a Product
- The given product is 15 × 16 × 17 × 18 × 20 × 21 × 24 × 25 × 27 × 28.
- To count the number of zeros at the end of the product, determine the number of times 10 is a factor.
- 10 = 2 × 5. Thus, count the factors of 5 and 2 in the product. The exponent of 5 determines the number of trailing zeros.
- The prime factorizations of the numbers in the product are:
- 15 = 3 × 5
- 16 = 24
- 17 = 17
- 18 = 2 × 32
- 20 = 22 × 5
- 21 = 3 × 7
- 24 = 23 × 3
- 25 = 52
- 27 = 33
- 28 = 22 × 7
- Counting factors of 5:
- 5 appears in 15, 20, and 25. This yields 1 + 1 + 2 = 4 factors of 5.
- Counting factors of 2:
- 2 appears in 16, 18, 20, 24, and 28. This results in 4 + 1 + 2 + 3 + 2 = 12 factors of 2.
- Since there are 4 factors of 5 and 12 factors of 2, the number of factors of 10 is limited by the smaller count, which is 4.
- Therefore, there are 4 trailing zeros in the product.
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Description
This quiz explores how to determine the number of trailing zeros in a product by counting the factors of 2 and 5. Using the given product of numbers, you will learn to identify the contributions of each factor and calculate the total number of zeros at the end. Perfect for reinforcing concepts in number theory and factorials.
