1. Which of the following are factors of 12? A. 1. 2. 3. 6. 9.12 C. 1. 3. 4. 6. S. 10 B. 1. 2. 3. 5. 6.12 D. 1. 2. 3. 4. 6.12 2. Which of the following are multiples of 8? A. 1, 2, 4, 8, 10, 12 C. 8, 16, 24, 36, 40 B. 8. 16, 24, 36. 45 D. S. 16, 24, 32, 40 3. What is a factor? A. A number multiplied by another number to find a product. B. The greatest factor that two or more numbers have in common. C. The smallest number that is a multiple of two or more numbers. D. The product of a given whole number and another whole number. 4. What is a multiple? A. A number multiplied by another number to find a product. B. The greatest factor that two or more numbers have in common. C. The smallest number that is a multiple of two or more numbers. D. The product of a given whole number and another whole number. 5. What is the LCM of 15 and 9? A. 3 B. 15 C. 45 D. 160 6. What is the GCF of 65, 80, and 105? A. 5 B. 8 C. 9 D. 10 7. What is the common factor of 20 and 35? A. 5 B.10 C. 18 D. 30 kont 8. What are the common multiples of 4, 5 and 8? A. 8, 10, 16 B. 16, 20, 24 C. 40, 80, 120 D. 50, 90, 100 9. If the GCF of 16 and 24 is 8, what is the GCF of 12 and 24? A. 8 B. 12 C. 14 D. 36 10. Criselda has 56 red flowers and 88 yellow flowers. She wants to make bouquets with the same number of red and yellow flowers in it. What is the greatest number of bouquets she can make? A. 8 B. 15 C. 18 D. 21
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Answer:
Write out the first few common multiples of 12 and of 16. Hence write out the first few common multiples of 12 and 16, and state their lowest common multiple.
b
Write out the first few multiples of 24. Hence write down the LCM of 12, 16 and 24?
c
What is the LCM of 12 and 15?
d
What is the LCM of 4, 6 and 9?
SOLUTION
a
The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144,…
The multiples of 16 are 16, 32, 48, 64, 80, 96, 112, 128, 144, 160,…
Hence the common multiples of 12 and 16 are 48, 96, 144,… and their LCM is 48.
b
The multiples of 24 are 0, 24, 48,… Hence the LCM of 12, 16 and 24 is 48.
c
The LCM of 12 and 15 is 60.
d
The LCM of 4, 6 and 9 is 36.
Step-by-step explanation:
We say that 6 is a factor of 18 because 18 can be factored as the product 18 = 6 × 3.
This can be restated in terms of the multiples of the previous section:
The statement that ‘6 is a factor of 18’ means that ‘18 is a multiple of 6.’
The number zero is a multiple of every number, so every number is a factor of zero. On the other hand, zero is the only multiple of zero, so zero is a factor of no numbers except zero. These rather odd remarks are better left unsaid, unless students insist. They should certainly not become a distraction from the nonzero whole numbers that we want to discuss.
The product of two nonzero whole numbers is always greater than or equal to each factor in the product. Hence the factors of a nonzero number like 12 are all less than or equal to 12. Thus whereas a positive whole number has infinitely many multiples, it has only finitely many factors.
The long way to find all the factors of 12 is to test systematically all the whole numbers less than 12 to see whether or not they go into 12 without remainder. The list of factors of 12 is
1, 2, 3, 4, 6 and 12.
It is very easy to overlook factors by this method, however. A far more efficient way, is to look for pairs of factors whose product is 12. Begin by testing all the whole numbers 1, 2, … that could be the smaller of a pair of factors with product 12,
1, 2, 3,…
We stop at 3 because 42 = 16 is greater than 12, so 4 cannot be the smaller of a pair.
Now we add, in reverse order, the complementary factor of each pair, that is, 12 ÷ 3 = 4, 12 ÷ 2 = 6 and 12 ÷ 1 = 12,
We can display these pairs of factors by writing the 12 dots in all possible rectangular arrays:
E3g27.pdf E3g28.pdf
1 × 12
2 × 6
3 × 4
For a larger number such as 60, the method recommended here has the following steps:
Test whether each whole number 1, 2, 3,… is a factor of 60.
Continue testing up to 7, because 82 = 64 is greater than 60.
Then write down each complementary factor in reverse order.
Thus the factors of 60 are
Answer:
2.3.6.9.12 C.1.3.4.6.S. 10 B.1.2.3.5.6.12
Step-by-step explanation:
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