Page 61 - Start Up Mathematics_6
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Example 25: Here are two different factor trees for 80. Write the missing numbers.
(a) (b)
80 80
40 ? 10
8
20 ? ? ?
?
4
? 4
2 ?
2 ?
Solution: (a) (b)
80 80
40 2 10
8
20 2 2 5 2
4
5 4
2 2
2 2
Example 26: Which factors of a number are not included in prime factorization of a composite
number? Explain with an example.
Solution: The number itself and 1 are not included in prime factorization of a composite number.
For example, 12 = 3 × 2 × 2, the number itself, i.e., 12 and 1 are not included in
prime factors.
Example 27: Write the smallest 4-digit number and express it in the form of its prime factors.
Solution: Smallest 4-digit number is 1,000.
Prime factors of 1,000 = 2 × 2 × 2 × 5 × 5 × 5.
Example 28: Find all the prime factors of 15,015 and arrange them in ascending order. Now state
the relation, if any, among the prime factors.
Solution: Prime factors of 15,015 = 3 × 5 × 7 × 11 × 13.
We observe that 15,015 is the product of 5 consecutive prime numbers.
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