490 as a product of its prime factors
The correct answer and explanation is:
The prime factorization of 490 is: 490=2×5×7×7490 = 2 \times 5 \times 7 \times 7
or equivalently, 490=2×5×72490 = 2 \times 5 \times 7^2
Explanation:
To find the prime factorization of 490, we begin by dividing it by the smallest prime number, 2, since 490 is an even number.
- Step 1: Divide by 2:
490÷2=245490 \div 2 = 245 Now, we are left with 245. - Step 2: Divide by 5:
Next, since 245 ends in a 5, it is divisible by 5.
245÷5=49245 \div 5 = 49 Now, we are left with 49. - Step 3: Divide by 7:
49 is a perfect square of 7, so we divide it by 7 twice.
49÷7=749 \div 7 = 7
7÷7=17 \div 7 = 1
Now that we have reached 1, we stop the division process. The prime factors of 490 are 2, 5, and 7, with 7 appearing twice. This gives us the prime factorization: 490=2×5×7×7or490=2×5×72490 = 2 \times 5 \times 7 \times 7 \quad \text{or} \quad 490 = 2 \times 5 \times 7^2
This shows the complete breakdown of 490 into its prime components.