Page 61 - ICSE Math 6

Example 17: Which factors of a composite number are not included in its prime factorization? Explain
with an example.

Solution: In the prime factorization of a composite number the number itself, its composite
factors and 1 are not included.
For example, 12 = 3 × 2 × 2
Here, we can see that the number itself, i.e., 12, its composite factors, i.e., 4 and 6, and
1 are not included in the prime factorization.

Example 18: Write the prime factorization of the smallest 4-digit number.
Solution: Smallest 4-digit number is 1,000.

Prime factorization of 1,000 = 2 × 2 × 2 × 5 × 5 × 5

Example 19: 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: The prime factorization of 15,015 = 3 × 5 × 7 × 11 × 13. So, all the prime factors of
15,015 arranged in ascending order are 3, 5, 7, 11 and 13.
We observe that each factor in the order is 2 more than the factor to the left of it.

EXERCISE 4.4

1. Find the prime factorization of the following.
(a) 2,904 (b) 1,500 (c) 3,969 (d) 9,317 (e) 2,907 (f) 4,641

2. Write the prime factorization of the greatest 3-digit number.
3. Write the prime factorization of the smallest 5-digit number.
4. Find the all prime factors of 20,570.
5. Check whether the prime factorization of the given numbers are correct or not. If it is not, write
the correct prime factorization.
(a) 60 = 2 × 2 × 15 (b) 20 = 2 × 2 × 5 (c) 72 = 6 × 12

6. Make a factor tree for: (a) 12 (b) 16 (c) 35

Highest Common Factor (HCF)

The HCF of two or more given numbers is the largest factor which
divides each of the given numbers completely. HCF is also known as Maths Info
GCD (greatest common divisor). For example, the greatest number The HCF of co-prime numbers
which divides 15 and 30 completely is 15. Therefore, 15 is the HCF is always 1.
of 15 and 30. We can find the HCF of the given numbers using the
following methods:
(a) Common Factor Method (b) Prime Factorization Method (c) Division Method

Common factor method
Step 1: Find all the factors of all the given numbers.

Step 2: From the factors obtained, select the factors common to all the given numbers.
Step 3: Out of the common factors, the largest factor is the HCF of the given numbers.

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