CBSE Class 6 Mathematics Factors And Multiples Worksheet

HCF ( HIGHEST COMMON FACTOR)

Explanation

The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also known as Greatest Common-divisor (GCD). The HCF of 20, 28 and 36 can also be found by prime factorisation of these numbers as follows:

Thus,
20 = 2 × 2 × 5;
28 = 2 × 2 × 7;
36 = 2 × 2 × 3 × 3;
The common factor of 20, 28 and 36 is 2(occurring twice). Thus, HCF of 20, 28 and 36 is 2 × 2 = 4.

How to find out HCF using division method(shortcut method)

To find out HCF of two given numbers using division method,

Step 1: Divide the larger number by the smaller number.
Step 2: Divisor of step 1 is divided by its remainder.
Step 3: Divisor of step 2 is divided by its remainder. Continue this process till we get zero as remainder.
Step 4: Divisor of the last step is the HCF.

Example 1: Find out HCF of 60 and 75

Hence HCF of 60 and 75 = 15

Worksheet Find the HCF of the numbers in each of the following, using the prime factorization method:
1) 84 ,98
2) 170,238
3) 504,980
4) 72,108,180

2. Find the HCF of the numbers in each of the following ,using the division method
1) 58,70
2) 399,437
3) 1045,1520
4) 1965,2096
5) 2241,2324v

3. Find the greatest number Which divides 615 and 963 leaving the remainder 6 in each case.

4.Reduce the following into lowest term
1.161/207
2.517/799
3.296/481 

Find the HCF of the numbers in each of the following, using the prime factorization method:

(1) 84, 98
Ans: All the factors of 84 are 2 x 2 x 3 x 7
All the factors of 98 are 2 x 7 x 7
Common factors of 84 and 98 are 2 x 7
Thus, the highest common factor of 84 and 98 is 7
Hence, HCF of 84 and 98= 7

(2) 170, 238
Ans: All the factors of 170 are 2 x 5 x 17
All the factors of 238 are 2 x 7 x 17
Common factors of 84 and 98 are 2 x 17
Thus, the highest common factor of 170 and 238 is 17
Hence, HCF of 84 and 98= 17

(3) 504, 980
Ans: All the factors of 504 are 2 x 2 x 2 x 3 x 3 x 7
All the factors of 980 are 2 x 2 x 5 x 7 x 7
Common factors of 504 and 980 are 2 x 2 x 7
Thus, the highest common factor of 504 and 980 is 7
Hence, HCF of 504 and 980= 7

(4) 72, 108, 180
Ans: All the factors of 72 are 2 x 2 x 2 x 3 x 3
All the factors of 108 are 2 x 2 x 3 x 3 x 3
All the factors of 180 are 2 x 2 x 3 x 3 x 5
Common factors of 72, 108 and 180 are 2 x 2 x 3 x 3
Thus, the highest common factor of 72, 108 and 180 is 3
Hence, HCF of 72, 108 and 180= 3

Find the HCF of the numbers in each of the following, using the division method:
(1) 58, 70
Ans: We have:

Hence, the HCF of 58 and 70 is 2.

(2) 399, 437
Ans: We have

Hence, the HCF of 399 and 437 is 19.

(3) 1045, 1520
Ans: We have

Hence, the HCF of 1045 and 1520 is 95.

(4) 1965, 2096
Ans: We have

Hence, the HCF of 1965 and 2096 is 131.

(5) 2241, 2324
Ans: We have

3 .find the greatest number which divides 615 and 963, leaving the remainder 6 in each case
Ans:
Since the remainder is 6 we have to find the number which exactly divides (615 -6) and (963 -6)
Required number = HCF of 609 and 957

Fill in the blanks :

Question. ___ is the multiple of every number.

Answer : Zero

Question. The greatest factor of every number is the number_____

Answer : Itself

Question. A ____ of number is exactly divisible by it.

Answer : Multiples

Question. Find the missing factors
8 × ? = 64
___× = 99
Answer : 8× 8 = 64
11×9 = 99

Question. Write the first five multiples of the following numbers.
a. 13
b. 17
c. 21
Answer : a. Five multiples of 13 are 13, 26, 39, 56, 65
b. Five multiples of 17 are 17, 34, 51, 68, 85
c. Five multiples of 21 are 21, 42, 63, 84, 105

Question. Write the smallest and greatest factors of 36.
Answer : All the factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Smallest factor of 36 = 1
Greatest factor of 36= 36

Question. Find the common factors of 12 and 24
Answer : Common factor of 12 and 24
Factor of 12 are
Factor of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Common factors of 12 and 24 are 1, 2, 3, 4, 6, and 12

Question. Write the factor of the following numbers.
a. 27
b. 32
c. 95
Answer : a. 27
1 × 27= 27
3 × 9 = 27
9 × 3 = 27
27 × 1 = 27
Hence, the factors of 27 are 1, 3, 9 and 27.
b. 32
1 × 32 = 32
2 × 16 = 32
4 × 8 = 32
8 × 4 = 32
16 × 2 =32
32 × 1 =32
Hence, the factors of 32 are 1,2,4, 8 16 and 32
c. 1 ×95 =95
5 × 19 = 95
19 × 5 =95
95 × 1 = 95
Hence, the factors of 95 are 1, 5, 19 and 95

Question. Find the common multiples of 15 and 30.
Answer : Common multiples of 15 and 30
Multiples of 15 are = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150
30 are = 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
The common multiples of 15 and 30 are 30, 60, 150……….

Choose the correct option in question no. 1, 2, 3 and 4

Q.1 Unique number (number which is neither prime nor composite) is
(a) 1
(b) 2
(c) 3
(d) 4

Q.2 The greatest prime number between 1 and 100 is
(a) 93
(b) 95
(c) 97
(d) 99

Q.3 The HCF of two consecutive even numbers is
(a) 2
(b) 3
(c) 4
(d) 5

Q.4 A number for which sum of all its factors is equal to twice the number is called
(a) Unique number
(b) Composite no.
(c) Perfect no.
(d) None

Q.5 Write all factors of each of the following numbers.
(i) 60
(ii) 125
(iii) 729

Q.6 Write first five multiples of each of the following numbers
(i) 25
(ii) 35
(iii) 40

Q.7 Write all prime numbers between
(i) 10 and 50
(ii) 70 and 90

Q.8 Express each of the following numbers as the sum of two odd primes
(i) 36
(ii) 42
(iii) 84

Q.9 Express each of the following numbers as the sum of three odd primes
(i) 31
(ii) 35
(iii) 49

Q.10 Express each of the following as the sum of twin primes
(i) 36
(ii) 84

Q.11 Find prime factorization of each of the following numbers
(i) 216
(ii) 420
(iii) 468
(iv) 945
(v) 7325

Q.12 Write the smallest 4 digit number and express it as a product of primes.

Q.13 Write the largest 4 digit number and give its prime factorization.

Q.14 Which factors are not included in the prime factorization of a composite number.
(i) 144, 198
(ii) 81, 117
(iii) 225, 450
(iv) 150, 140, 210
(v) 84, 120, 138

Q.15 Determine the HCF of the following numbers by division method
(i) 300, 450
(ii) 399, 437
(iii) 1045, 1520

Q.16 Determine the LCM of the numbers given below
(i) 48, 60
(ii) 18, 17
(iii) 15, 30, 90
(iv) 56, 65, 85

Q.17 The LCM and HCF of two numbers are 180 and 6 respectively. If one of the numbers is 30, find the other number

Q.18 The HCF of two numbers is 16 and their product is 3072. Find their LCM

Q1 Complete the patterns
(a) Multiples of 11→11,_______,_______,_______,_______
(b) Multiples of 15→ 15, _____, _____, _____, ______
(c) 8 ,_____,24,______,______,48,___,___,72
(d) 20, _____,_____,_____,100,_____,140,_____,180

Q2 Choose the correct answer
(a) All numbers with 0,2,4,6,8 in the ones place are multiples of__________ (2,3,7,9)
(b) All numbers with 5 or 0 in the ones place are multiples of ________ (2, 3, 5, 10)
(c) LCM of 7 and 14 is _______ (2, 7, 14, and 15)
(d) All numbers with 0 in the ones place are multiples of_____ (2, 5, 10, 3)

Q3 Write all the multiples of 7 which lie between 32 and 80?

Q4 Write the first five multiples of 6 and 12. Find their common multiples and the LCM.

Q5 Write the greatest
(a) 2-digit multiple of 3 _________
(b) 3-digit multiple of 2_________

Q6 Encircle the numbers which are multiples of 2.Put a square around the multiples of 4.List their common multiples
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Common multiples of 2 and 4 are_______________ 

Q7 Write the
(a) first two common multiples of 4 and 5 ___________
(b) first two common multiples of 6 and 8 ___________
(c) first two common multiples of 2 , 3 and 5 ___________