Looking for engaging and educational practice worksheets on Factors for Class 5 students? This post has you covered! We’ve compiled a set of free worksheets that cover the following essential topics:
- The Rule of Divisibility: Understand the tricks to determine if a number is divisible by another.
- Prime Numbers: Learn to identify numbers that have only two factors—1 and itself.
- Composite Numbers: Differentiate composite numbers from primes with ease.
- Prime Factorization: Break down numbers into their prime factors step by step.
- Power of 10 and 2: Explore the concept of exponents with these special numbers.
- Highest Common Factor (HCF): Find the greatest factor common to two or more numbers.
- Finding HCF using Prime Factorization: Master this reliable method to determine the HCF.
Each worksheet is thoughtfully designed to reinforce understanding, enhance problem-solving skills, and build confidence in tackling factors-related problems.
Table of Contents
Quick Summary of Factors for Class 5 Students
Rule of Divisibility for Numbers
Understanding the rules of divisibility makes it easier to check if one number can be divided by another without performing long division. Below are the divisibility rules for some important numbers:
Divisibility by 2:
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
Examples:
- 246 is divisible by 2 because the last digit is 6 (even).
- 123 is not divisible by 2 because the last digit is 3 (odd).
Divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Examples:
- For 123, the sum of the digits is 1+2+3=61 + 2 + 3 = 61+2+3=6, which is divisible by 3.
- For 124, the sum of the digits is 1+2+4=71 + 2 + 4 = 71+2+4=7, which is not divisible by 3.
Divisibility by 4:
A number is divisible by 4 if the last two digits of the number form a number divisible by 4.
Examples:
- 316 is divisible by 4 because the last two digits, 16, are divisible by 4.
- 123 is not divisible by 4 because the last two digits, 23, are not divisible by 4.
Divisibility by 5:
A number is divisible by 5 if its last digit is 0 or 5.
Examples:
- 150 is divisible by 5 because the last digit is 0.
- 133 is not divisible by 5 because the last digit is 3.
Divisibility by 6:
A number is divisible by 6 if it is divisible by both 2 and 3.
Examples:
- 120 is divisible by 6 because it is divisible by 2 (last digit is 0) and by 3 (sum of digits is 1+2+0=31 + 2 + 0 = 31+2+0=3, divisible by 3).
- 121 is not divisible by 6 because it is not divisible by 2 (last digit is odd).
Divisibility by 8:
A number is divisible by 8 if the last three digits form a number divisible by 8.
Examples:
- 1,024 is divisible by 8 because the last three digits, 024, are divisible by 8.
- 123 is not divisible by 8 because the last three digits, 123, are not divisible by 8.
Divisibility by 9:
A number is divisible by 9 if the sum of its digits is divisible by 9.
Examples:
- For 81, the sum of the digits is 8+1=98 + 1 = 98+1=9, which is divisible by 9.
- For 123, the sum of the digits is 1+2+3=61 + 2 + 3 = 61+2+3=6, which is not divisible by 9.
Divisibility by 10:
A number is divisible by 10 if its last digit is 0.
Examples:
- 230 is divisible by 10 because the last digit is 0.
- 235 is not divisible by 10 because the last digit is 5.
Divisibility by 11:
A number is divisible by 11 if the difference between the sum of digits in odd places and the sum of digits in even places is divisible by 11.
Examples:
- For 121, the difference is 1+1−2=01 + 1 – 2 = 01+1−2=0, which is divisible by 11.
- For 123, the difference is 1+3−2=21 + 3 – 2 = 21+3−2=2, which is not divisible by 11.
Prime Numbers
Prime numbers are numbers that have only two factors: 1 and the number itself. Examples: 2, 3, 5, 7, 11.
Composite Numbers
Composite numbers have more than two factors. Examples: 4, 6, 8, 9, 12.
Prime Factorization
Prime factorization means breaking a number into a product of its prime numbers.
For example:
- The prime factorization of 12 is 2 × 2 × 3.
Power of 10 and 2
When multiplying the same number many times, we use powers.
For example:
- 10210^2102 means 10×10=10010 × 10 = 10010×10=100.
- 232^323 means 2×2×2=82 × 2 × 2 = 82×2×2=8.
Highest Common Factor (HCF)
The HCF is the largest factor that two or more numbers have in common.
Find HCF Using Prime Factorization
To find the HCF:
- Step 1: Find the prime factorization of each number.
- Step 2: Identify the common prime factors.
- Step 3: Multiply the common prime factors together.
Example:
For 12 and 18,
- Prime factorization of 12 = 2 × 2 × 3
- Prime factorization of 18 = 2 × 3 × 3
Common factors = 2 × 3
HCF = 6
This is how factors help us understand numbers better!
Disclaimer:
Please don’t rely solely on the answer keys provided. As a human, I might have made mistakes, so use your judgment to verify answers. These worksheets are free to download and use for personal purposes. Kindly refrain from using them for commercial purposes.
Download the worksheets now and empower your Class 5 students to excel in mathematics!
