Find all the Prime Factors of 112 using a factor tree.
The correct answer and explanation is:
To find the prime factors of 112 using a factor tree, start by dividing 112 by the smallest prime number, which is 2.
- Step 1: Divide 112 by 2: 112÷2=56112 \div 2 = 56 So, the first factor is 2, and now we continue with 56.
- Step 2: Divide 56 by 2: 56÷2=2856 \div 2 = 28 Another factor of 2 is found, and now we continue with 28.
- Step 3: Divide 28 by 2: 28÷2=1428 \div 2 = 14 We have another factor of 2, and now we continue with 14.
- Step 4: Divide 14 by 2: 14÷2=714 \div 2 = 7 Another factor of 2 is found, and now we are left with 7.
- Step 5: Now, 7 is a prime number, so we stop here.
The prime factors of 112 are 2, 2, 2, 2, and 7. To write this more succinctly, we express it as: 112=24×7112 = 2^4 \times 7
Explanation:
A factor tree is a way of breaking down a number into its prime factors, starting with the smallest prime number and working upwards. The prime factorization of a number gives us a list of prime numbers that multiply together to make that number.
In this case, 112 is divisible by 2 repeatedly, showing that 2 is a factor of 112. Once the number is reduced to 7, a prime number, we stop the factorization process. The factorization of 112 is written as 24×72^4 \times 7, meaning that 112 is the product of four 2’s and one 7.
This process helps identify the simplest form of prime factors, which are often useful in various mathematical operations, including finding the greatest common divisor (GCD), least common multiple (LCM), or simplifying fractions.