To solve the problem of factoring the given numbers into their prime factors, we will break each number down step by step using division by prime numbers. Let's go through each number:
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1 a. 5
-
Step 1: Check if 5 is divisible by any prime number less than itself.
-
Result: 5 is a prime number, so its only prime factor is itself.
-
Prime Factorization: \( 5 = 5 \)
---
1 b. 98
-
Step 1: Divide by the smallest prime number, 2.
\[
98 \div 2 = 49
\]
-
Step 2: Now factor 49. The next smallest prime number is 7.
\[
49 \div 7 = 7
\]
-
Step 3: 7 is a prime number.
-
Prime Factorization: \( 98 = 2 \times 7 \times 7 = 2 \times 7^2 \)
---
1 c. 42
-
Step 1: Divide by the smallest prime number, 2.
\[
42 \div 2 = 21
\]
-
Step 2: Now factor 21. The next smallest prime number is 3.
\[
21 \div 3 = 7
\]
-
Step 3: 7 is a prime number.
-
Prime Factorization: \( 42 = 2 \times 3 \times 7 \)
---
2 a. 53
-
Step 1: Check if 53 is divisible by any prime number less than itself (2, 3, 5, 7, etc.).
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Result: 53 is not divisible by any of these primes and is therefore a prime number.
-
Prime Factorization: \( 53 = 53 \)
---
2 b. 27
-
Step 1: Divide by the smallest prime number, 3.
\[
27 \div 3 = 9
\]
-
Step 2: Now factor 9. Divide by 3 again.
\[
9 \div 3 = 3
\]
-
Step 3: 3 is a prime number.
-
Prime Factorization: \( 27 = 3 \times 3 \times 3 = 3^3 \)
---
2 c. 5
-
Step 1: Check if 5 is divisible by any prime number less than itself.
-
Result: 5 is a prime number, so its only prime factor is itself.
-
Prime Factorization: \( 5 = 5 \)
---
3 a. 75
-
Step 1: Divide by the smallest prime number, 3.
\[
75 \div 3 = 25
\]
-
Step 2: Now factor 25. Divide by 5.
\[
25 \div 5 = 5
\]
-
Step 3: 5 is a prime number.
-
Prime Factorization: \( 75 = 3 \times 5 \times 5 = 3 \times 5^2 \)
---
3 b. 46
-
Step 1: Divide by the smallest prime number, 2.
\[
46 \div 2 = 23
\]
-
Step 2: Now factor 23. Check if 23 is divisible by any prime number less than itself.
-
Result: 23 is a prime number.
-
Prime Factorization: \( 46 = 2 \times 23 \)
---
3 c. 57
-
Step 1: Divide by the smallest prime number, 3.
\[
57 \div 3 = 19
\]
-
Step 2: Now factor 19. Check if 19 is divisible by any prime number less than itself.
-
Result: 19 is a prime number.
-
Prime Factorization: \( 57 = 3 \times 19 \)
---
Final Answers:
\[
\boxed{
\begin{array}{ccc}
1 \text{a. } 5 & 1 \text{b. } 2 \times 7^2 & 1 \text{c. } 2 \times 3 \times 7 \\
2 \text{a. } 53 & 2 \text{b. } 3^3 & 2 \text{c. } 5 \\
3 \text{a. } 3 \times 5^2 & 3 \text{b. } 2 \times 23 & 3 \text{c. } 3 \times 19 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of factor tree worksheet 5th grade.
