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In which of the following expressions, prime factorization has been done?
(i) 24 = 2 x 3 x 4 is not a prime factorization as 4 is not a prime number.
(ii) 56 = 1 x 7 x 2 x2 x 2 is not a prime factorization as 1 is not a prime number.
(iii) 70 = 2 x 5 x 7 is a prime factorization as 2, 5, and 7 are prime numbers.
(iv) 54 = 2 x 3 x 9 is not a prime factorization as 9 is not a prime number.
Determine prime factorization of each of the following numbers:
(i) 216
We have:
Therefore, Prime factorization of 216 = 2 x 2 x 2 x 3 x 3
(ii) 420
Therefore, Prime factorization of 420 = 2 x 2 x 3 x 5 x 7
(iii) 468
Therefore, Prime factorization of 468 = 2 x 2 x 3 x 3 x 13
(iv) 945
Therefore, Prime factorization of 945 = 3 x 3 x 3 x 5 x 7
(v) 7325
Therefore, Prime factorization of 732 5= 5 x 5 x 293
(vi) 13915
Therefore, Prime factorization of 13915 = 5 x 11 x 11 x 23
Write the smallest 4-digit number and express it as a product of primes.
The smallest 4-digit number is 1000.
1000 = 2 x 500
= 2 × 2 × 250
= 2 × 2 × 2 × 125
= 2 × 2 × 2 × 5 × 25
= 2 × 2 × 2 × 5 × 5 × 5
Therefore, 1000 = 2 × 2 × 2 × 5 × 5 × 5
Write the largest 4-digit number and express it as product of primes.
The largest 4-digit number is 9999.
Hence, the largest 4-digit number 9999 can be expressed in the form of its prime factors as 3 x 3 x 11 x 101.
Find the prime factors of 1729. Arrange the factors in ascending order, and find the relation between two consecutive prime factors.
The given number is 1729.
Thus, the number 1729 can be expressed in the form of its prime factors ass 7 x 13 x19.
Relation between its two consecutive prime factors:
The consecutive prime factors of the given number are 7, 13 and 19.
Clearly, 13 – 7 = 6 and 19 – 13 =6
Here, in two consecutive prime factors, the latter is 6 more than the previous one.
Which factors are not included in the prime factorization of a composite number?
1 and the number itself are not included in the prime factorization of a composite number.
Example: 4 is a composite number.
Prime factorization of 4 = 2 x 2.
Here are two different factor trees for 60. Write the missing numbers:
(i) Since 6 = 2 x 3 and 10= 5 x 2. We have:
(ii) Since 60 = 30 x 2.
30= 10 x 3 and 10 = 5 x 2 we have:
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Chapter 2: Playing With Numbers – Exercise...