prime factorization of 980
2 squared X 5 X 7 squared.
2x2x5x7x7=980
980 is not a prime number
To find the prime factorization of 980, we need to determine the prime numbers that can divide evenly into 980.
One method to find the prime factorization is to start dividing 980 by the smallest prime number, which is 2, repeatedly until we can no longer divide evenly.
1. Divide 980 by 2: 980 ÷ 2 = 490.
- 2 is a prime factor of 980.
- The result is 490.
2. Divide 490 by 2: 490 ÷ 2 = 245.
- 2 is a prime factor of 980.
- The result is 245.
3. Divide 245 by 2: 245 ÷ 2 = 122.5 (not divisible evenly).
Since 2 is no longer divisible into 245, we move on to the next prime number, which is 3.
4. Divide 245 by 3: 245 ÷ 3 = 81.67 (not divisible evenly).
Next, we try dividing by the next prime number, which is 5.
5. Divide 245 by 5: 245 ÷ 5 = 49.
- 5 is a prime factor of 980.
- The result is 49.
We continue dividing until we have a prime factor greater than the square root of 980, so we try dividing by 7.
6. Divide 49 by 7: 49 ÷ 7 = 7.
- 7 is a prime factor of 980.
- The result is 7.
Now, we are left with the final result of 7. Since 7 is a prime number, it is also a prime factor of 980.
Therefore, the prime factorization of 980 is 2 * 2 * 5 * 7, which can be written as 2^2 * 5 * 7.