AP 5th Maths Workbook Solutions – 4. Multiples and Factors (2026-27)

4 Multiples and Factors

Worksheet - 1

Sub Topic: Divisibility Rules for 2, 5, 10

I) Observe the following numbers in tables. Put (✓) if the number is divisible by the given number, if not put (×).

a)

Numberయ	Digit in ones place	Is it divisible by 2?
587	7	×
2358	8	✓
2200	0	✓
8495	5	×

b)

Number	Digit in ones place	Divisible by 2	Divisible by 10
6806	6	✓	×
5800	0	✓	✓
7805	5	×	×
5890	0	✓	✓

II) Verify which of the following numbers is divisible by 2, 5 and 10 without doing actual division.

• a) 4580
  Divisible by 2: Yes, Divisible by 5: Yes, Divisible by 10: Yes
• b) 896
  Divisible by 2: Yes, Divisible by 5: No, Divisible by 10: No
• c) 8000
  Divisible by 2: Yes, Divisible by 5: Yes, Divisible by 10: Yes
• d) 780
  Divisible by 2: Yes, Divisible by 5: Yes, Divisible by 10: Yes

III) Observe the number chart 1-100

Follow chart instructions: draw square for numbers divisible by 2 only, circle for numbers divisible by 5 only, and triangle for numbers divisible by 2, 5, and 10.

Worksheet - 2

IV) Observe the following statements. State which are correct?

• i) If a number is divisible by 10, it should be divisible by 2 and 5.
  ii) When a number is divisible by 2 it should be odd number.
  iii) A number is divisible by 5, the last digit of that number must be 0 or 5.
  Answer: C) i, iii are correct

Worksheet - 3

Sub Topic: Divisibility Rules

1) Circle the following numbers which are divisible by 4.

a) 1108, c) 1600, d) 4256, e) 8888

2) Circle the following numbers which are divisible by 8.

b) 28864, c) 29632, d) 15800

II) Check whether the following numbers are divisible by 4 or not?

Number	Yes or No ు	Reason
348	Yes	48 is a multiple of 4
722	No	22 is not a multiple of 4
1200	Yes	Last two digits form 00
8518	No	18 is not a multiple of 4
27616	Yes	16 is a multiple of 4

III) Observe the following numbers, which number should be added to make them divisible by 8.

• a) 23410
  Add 6
• b) 57140
  Add 4
• c) 68902
  Add 6

IV) Write any 4 three digit numbers that are exactly divisible by 4 and 8.

104, 120, 136, 200

Worksheet - 4

Sub Topic: Multiples and common multiples

I).1 Write the first five multiples of the following numbers.

• a) 5: 5, 10, 15, 20, 25
• b) 8:
  8, 16, 24, 32, 40
• c) 9:
  9, 18, 27, 36, 45

2. Circle the multiples of 12 among the given numbers.

48, 56, 58, 78, 84, 86, 96

48, 84, 96

II) Write the first 10 multiples of the given numbers.

• Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
• Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
• Common multiples of 5 and 6 = 30, 60

III) Monkey and Rabbit are jumping on a number line.

• a) Monkey jumps (multiple of 4):
  4, 8, 12, 16, 20, 24, 28, 32, 36, 40
• b) Rabbit jumps (multiple of 6):
  6, 12, 18, 24, 30, 36
• c) Monkey and Rabbit meeting points:
  12, 24, 36

IV) I am a multiple of 4. When added 5 to me, I am a multiple of 7. Which number am I?

23 (Since 23 + 5 = 28, which is a multiple of 7)

V) Match the leaves that show multiples of the number written on the pot with their stem.

Match leaves to pots based on multiples of numbers on pots.

Worksheet - 5

Sub Topic: Least Common Multiple

I) Fill the table.

Number	First 10 multiples	Common multiples	LCM
10	10, 20, 30, 40, 50, 60, 70, 80, 90, 100	30, 60, 90	30
15	15, 30, 45, 60, 75, 90, 105, 120, 135, 150
20	20, 40, 60, 80, 100, 120, 140, 160, 180, 200

II) Find the least common multiple (L.C.M) of following numbers.

• a) Multiples of 4: 4, 8, 12, 16, 20, 24, ...
  Multiples of 6: 6, 12, 18, 24, ...
  Common multiples: 12, 24, ...
  LCM = 12
• b) Multiples of 6: 6, 12, 18, 24, 30, ...
  Multiples of 24: 24, 48, 72, ...
  Common multiples: 24, 48, ...
  LCM = 24

Worksheet - 6

III) Observe the following multiples of different numbers and classify them in the table.

Numbers	Multiples
4	4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68
5	5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70
6	6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66

IV) Match the following multiples with their LCM.

NUMBERS	Ans	LCM
i) 16, 24	( C )	A) 24
ii) 8, 6	( C )	B) 20
iii) 14, 28	( D )	C) 48
iv) 10, 20	( B )	D) 28

Worksheet - 7

Sub Topic: Factors

I) Find all the factors of the given numbers?

• a) 18
  1, 2, 3, 6, 9, 18
• b) 26
  1, 2, 13, 26
• c) 66
  1, 2, 3, 6, 11, 22, 33, 66
• d) 38
  1, 2, 19, 38

II) Identify factors of 36 and 24 and colour them.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

III) Sum of the prime numbers between 1 to 20?

Primes: 2, 3, 5, 7, 11, 13, 17, 19. Sum = 77.
Answer: C) 77

Worksheet - 8

IV) ACTIVITY: Observe the grid.

• a) Identify 12 boxes to form a rectangle.
  Done
• b) Width of this rectangle is 1 boxes.
• c) Length of the rectangle is 12 boxes.

Rectangle	Length [boxes]	Breadth [boxes]	Total boxes
1	12	1	$12 \times 1 = 12$
2	6	2	$6 \times 2 = 12$
3	4	3	$4 \times 3 = 12$

Worksheet - 9

Sub Topic: Prime Factorisation

I) Write each of the following as a product of prime factors.

• 1. a) 38
  $2 \times 19$
• b) 48
  $2 \times 2 \times 2 \times 2 \times 3$
• 2. a) 64
  $2 \times 2 \times 2 \times 2 \times 2 \times 2$
• b) 56
  $2 \times 2 \times 2 \times 7$

II) Observe the prime factorisation through division method. Identify mistake and correct it.

a) For 64: $2 \times 2 \times 2 \times 2 \times 2 \times 2$
b) For 72: $2 \times 2 \times 2 \times 3 \times 3$

III) The prime factorisation of a number is $2 \times 2 \times 2 \times 3 \times 5$. Find the number.

120

IV) Prime factorisation of the number 98 is.

Answer: B) $2 \times 7 \times 7$

Worksheet - 10

Sub Topic: Highest Common Factor

I) Write the factors and find HCF.

• a) Factors of 12 and 26
  Factors of 12: 1, 2, 3, 4, 6, 12
  Factors of 26: 1, 2, 13, 26
  Common factors: 1, 2
  HCF = 2
• b) Factors of 21 & 15
  Factors of 21: 1, 3, 7, 21
  Factors of 15: 1, 3, 5, 15
  Common factors: 1, 3
  HCF = 3

II) Match the following numbers with their H.C.F.

Numbers	Ans	HCF
i) 10, 20	( C )	A) 8
ii) 8, 6	( D )	B) 14
iii) 14, 28	( B )	C) 10
iv) 16, 24	( A )	D) 2

III) Write factors of 40, 20, 60 in the table and colour HCF.

HCF of 40, 20, and 60 is 20.

IV) The Highest Common Factor (H.C.F.) of 4 and 6 is.

Answer: A) 2

Worksheet - 11

Sub Topic: L.C.M and H.C.F

I) Use prime factorisation method to find LCM and HCF.

• 1) 4, 24
  H.C.F. = 4, L.C.M. = 24
• 2) 4, 24
  H.C.F. = 4, L.C.M. = 24

II) Use division method to find LCM and HCF.

• 3) 24, 36
  H.C.F. = 12, L.C.M. = 72
• 4) 10, 16
  H.C.F. = 2, L.C.M. = 80

Worksheet - 12

III, IV, V) Baba attends music classes every 5th day and dance classes every 3rd day...

• a) What information is given?
  Music class every 5th day, dance class every 3rd day, both on May 5th.
• b) What is to be found?
  Next date of attending both classes together.
• c) Which process do you follow?
  Finding LCM of 3 and 5.
• d) Next date:
  May 20th

Worksheet - 13

Sub Topic: Application of LCM and HCF

I) Find the least number which when evenly divided by 10, 20 and 15 leave remainder 5.

• Given numbers: 10, 15, 20
• Remainder: 5
• Process: Find LCM of 10, 15, 20 and add 5.
• Required least number:
  60 + 5 = 65

II) Amusement park gift bags (Hat every 2nd, T-shirt every 7th, Ball every 10th visitor)

LCM of 2, 7, 10 = 70. 70th visitor receives all three items.

Worksheet - 14

III) Find the largest number that divides 96 and 144 without leaving a remainder.

HCF of 96 and 144 = 48

IV) What is the least number that should be added to 3 so that the result is divisible by 15, 21, and 25?

LCM of 15, 21, 25 = 525. Number = 525 - 3 = 522

Self Assessment

I) Find the factors of 72 through Division method.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

II) Which of these is the correct prime factorisation of 60?

Answer: B) $2 \times 5 \times 6$

III) Write the following statements TRUE or FALSE.

Statement	Ans
a) If the last two digits of a number are divisible by 4, the number is divisible by 4.	True
b) 2 is the only odd prime number.	False
c) A number which has more than two factors is called a prime number.	False
d) A number which has two factors one and itself is called a composite number.	False
e) If the last three digits of a number are divisible by 8, then the entire number is divisible by 8.	True

IV) Vinay says, "Every even number is a multiple of 4." Do you agree? - Yes / No

Answer: No
Justification: 6 is an even number, but it is not a multiple of 4.

V) Prime factorisation tree of 24 (Mahir vs Bhanu)

Mahir's answer is correct (A = 2, B = 3).

VI) The H.C.F. of two numbers is 9 and their L.C.M. is 30. If one number is 9, find other number.

Other number = 30