Place Value Definition Chart and Solved Examples for Class 2
The concept of Factors of 343 is important for students learning number theory and helps develop skills in divisibility, prime factorization, and problem solving. Understanding factors is essential for school exams, competitive exams, and for building a foundation for advanced topics in mathematics.
What are Factors of 343?
A factor of a number is any whole number that divides the number completely, leaving no remainder. The factors of 343 are the numbers you can multiply in pairs to get 343 as the product. Factors are used in identifying divisibility, simplifying fractions, and solving equations. Recognizing factors quickly is a key arithmetic skill for exams and real life.
The positive factors of 343 are: 1, 7, 49, and 343.
Prime Factorization of 343
Prime factorization is expressing a number as a product of its prime factors. For 343:
- First, divide by the smallest prime number: 343 is not divisible by 2, 3, or 5.
- Divide by 7: 343 ÷ 7 = 49
- 49 is also divisible by 7: 49 ÷ 7 = 7, and 7 is a prime number.
So, the prime factorization of 343 is:
343 = 7 × 7 × 7 = 73
| Step | Division | Result |
|---|---|---|
| 1 | 343 ÷ 7 | 49 |
| 2 | 49 ÷ 7 | 7 |
| 3 | 7 ÷ 7 | 1 |
Factor Pairs of 343
A factor pair consists of two numbers that, when multiplied, give 343. The factor pairs of 343 are:
- 1 × 343
- 7 × 49
- 49 × 7
- 343 × 1
Notice that each pair contains two factors whose product is 343. This understanding makes calculations easier, especially when dividing items into equal groups.
Worked Examples
Let’s look at how to find and use the factors of 343 in real situations.
-
Find all the factors of 343.
- Start from 1. 343 ÷ 1 = 343, so both 1 and 343 are factors.
- Try 7. 343 ÷ 7 = 49, so 7 and 49 are factors.
- 49 × 7 = 343 already found.
- 343 ÷ 49 = 7 (already listed). None of the other numbers between 1 and 49 divides 343 without a remainder.
- So, 1, 7, 49, 343 are all the factors.
-
Distribute 343 marbles equally into bags. What are the possible sizes for the bags?
- The number of marbles per bag can be any factor of 343: 1 marble per bag (343 bags), 7 per bag (49 bags), 49 per bag (7 bags), or 343 per bag (1 bag).
Practice Problems
- List all positive factors of 343.
- Is 14 a factor of 343? Why or why not?
- What is the sum of all the factors of 343?
- Find the greatest common factor (GCF) of 343 and 49.
- If 343 apples are divided equally among 7 people, how many will each person get?
Common Mistakes to Avoid
- Confusing multiples and factors: Remember, factors divide 343 exactly; multiples of 343 are 343, 686, 1029, etc.
- Missing 1 and 343 as factors: Every whole number is a factor of itself, and 1 is a universal factor.
- Assuming even numbers must be factors: 343 is odd, so only odd factors are possible.
Real-World Applications
Knowing the factors of 343 can help in real-life situations such as dividing 343 items evenly among groups (for example, distributing candies, marbles, or arranging objects in rows and columns). This concept is also used in puzzle questions and helps understand the basics of prime numbers in higher mathematics. At Vedantu, such skills are reinforced with fun, interactive worksheets and teacher explanations to make factoring easy and rewarding.
In this page, you’ve learned what the factors of 343 are, how to find them using prime factorization, factor pairs, and the significance of these skills for exams and everyday situations. Mastering factors makes it easier to understand many Maths topics and sets a strong foundation for future learning. For more maths concepts, explore Vedantu’s full range of resources, like Factors of 49 or Factors of 216.
FAQs on Understanding Place Value in Grade 2 Math
1. What is place value in Maths?
Place value is the value of a digit based on its position in a number. In the base-10 number system, each place represents a power of 10.
- Ones = 1
- Tens = 10
- Hundreds = 100
- Thousands = 1,000
2. How do you find the place value of a digit in a number?
To find the place value of a digit, multiply the digit by the value of its position. Each position increases by a factor of 10 as you move left.
- Step 1: Identify the digit.
- Step 2: Identify its position (ones, tens, hundreds, etc.).
- Step 3: Multiply the digit by the place value.
3. What is the difference between place value and face value?
The face value of a digit is the digit itself, while the place value depends on its position in the number.
- Face value: The actual digit (e.g., 7 in 276 is 7).
- Place value: The digit multiplied by its position (7 in 276 is 70).
4. What is a place value chart?
A place value chart is a table that shows the value of each digit based on its position in a number. It helps learners organize digits correctly.
- Thousands
- Hundreds
- Tens
- Ones
- 3 in thousands
- 4 in hundreds
- 5 in tens
- 2 in ones
5. How do you write a number in expanded form using place value?
Expanded form shows a number as the sum of each digit multiplied by its place value.
- Break the number into place values.
- Write each digit times its place value.
- Add them together.
6. Why is place value important in Maths?
Place value is important because it helps us understand the size and value of numbers. It is the foundation for addition, subtraction, multiplication, and division.
- Helps in comparing numbers
- Supports regrouping (carrying and borrowing)
- Makes reading large numbers easier
7. How do you compare numbers using place value?
To compare numbers using place value, compare digits starting from the highest place value. The number with the greater digit in the highest place is larger.
- Step 1: Compare thousands.
- Step 2: If equal, compare hundreds.
- Step 3: Continue to tens and ones.
8. What is the place value of digits after the decimal point?
The place value of digits after the decimal point decreases by powers of 10 and represents parts of a whole.
- Tenths = 1/10
- Hundredths = 1/100
- Thousandths = 1/1000
9. What are common mistakes when learning place value?
A common mistake in place value is confusing the digit with its value. Students often read 407 as forty-seven instead of four hundred seven.
- Ignoring zero as a placeholder
- Misreading large numbers
- Confusing place value with face value
10. Can you give an example of place value in real life?
Place value is used in real life whenever we deal with money, measurements, or large numbers. For example, in $2,345:
- 2 represents 2,000 dollars
- 3 represents 300 dollars
- 4 represents 40 dollars
- 5 represents 5 dollars
