CBSE Class 5 Mathematics Be My Multiple Worksheet Set 05

Write the prime factorization for the following numbers

Question 1(a). 40
Answer: Prime factorization of 40:
\(40 = 2 \times 20\)
\(40 = 2 \times 2 \times 10\)
\(40 = 2 \times 2 \times 2 \times 5 = 2^3 \times 5\)
In simple words: Break down the number into smaller factors until all factors are prime numbers.

Exam Tip: Always start dividing by the smallest prime number, which is 2, and continue until you cannot divide further.

Question 1(b). 78
Answer: Prime factorization of 78:
\(78 = 2 \times 39\)
\(78 = 2 \times 3 \times 13\)
In simple words: Divide 78 by 2 to get 39, then split 39 into prime factors 3 and 13.

Exam Tip: Check divisibility rules carefully. Since 78 ends in an even number, it is divisible by 2.

Question 1(c). 120
Answer: Prime factorization of 120:
\(120 = 2 \times 60\)
\(120 = 2 \times 2 \times 30\)
\(120 = 2 \times 2 \times 2 \times 15\)
\(120 = 2 \times 2 \times 2 \times 3 \times 5 = 2^3 \times 3 \times 5\)
In simple words: Repeatedly divide by 2 and then by 3 and 5 until only prime numbers remain.

Question 1(d). 52
Answer: Prime factorization of 52:
\(52 = 2 \times 26\)
\(52 = 2 \times 2 \times 13 = 2^2 \times 13\)
In simple words: Divide 52 by 2 twice to get 13, which is a prime number.

Exam Tip: Memorize prime numbers up to 20 to easily identify when a number cannot be factored further.

Using the factor tree write the prime factorization for the following

Question 2(a). 72
Answer: Factor tree representation and prime factorization of 72:
\(72 = 2 \times 36\)
\(36 = 2 \times 18\)
\(18 = 2 \times 9\)
\(9 = 3 \times 3\)
Therefore, prime factorization = \(2 \times 2 \times 2 \times 3 \times 3 = 2^3 \times 3^2\)
In simple words: Grow the factor tree by branching each number into two factors until all branch tips are prime numbers.

Exam Tip: Draw the branches clearly in the box to represent the factor tree visually.

Question 2(b). 24
Answer: Factor tree representation and prime factorization of 24:
\(24 = 2 \times 12\)
\(12 = 2 \times 6\)
\(6 = 2 \times 3\)
Therefore, prime factorization = \(2 \times 2 \times 2 \times 3 = 2^3 \times 3\)
In simple words: Split 24 into 2 and 12, then continue branching until all factors are prime.

Exam Tip: Verify your final product: \(8 \times 3 = 24\), which matches the original number.