Find the prime factorization of each number and write it in exponential form from lowest number to highest 490
The correct answer and explanation is:
To find the prime factorization of 490, we need to break it down into its prime factors. Here’s the step-by-step process:
- Start by dividing 490 by the smallest prime number, which is 2. 490÷2=245490 \div 2 = 245 So, 2 is a factor of 490.
- Now, 245 is odd, so it’s not divisible by 2. Let’s try dividing by the next smallest prime number, which is 5. 245÷5=49245 \div 5 = 49 So, 5 is a factor of 490.
- Now, 49 is not divisible by 5, so we check the next prime number, 7. 49÷7=749 \div 7 = 7 So, 7 is a factor of 49.
- Finally, 7 is a prime number, so we stop here.
Thus, the prime factorization of 490 is: 490=2×5×7×7=2×5×72490 = 2 \times 5 \times 7 \times 7 = 2 \times 5 \times 7^2
The prime factorization in exponential form is: 21×51×722^1 \times 5^1 \times 7^2
Explanation:
Prime factorization involves breaking down a number into its basic prime factors. We start with the smallest prime (2) and continue dividing by primes like 3, 5, 7, and so on until all factors are prime. The prime factorization of 490 shows that 2, 5, and 7 are the prime factors. Since 7 appears twice, it is expressed as 727^2.
Prime factorization is useful for simplifying fractions, finding the greatest common divisor (GCD), and least common multiple (LCM) of numbers. This is a key concept in number theory and arithmetic operations.