Find the prime factorisation of 650.

To find the prime factorisation of 650, we need to determine the prime numbers that multiply together to give us 650.

Step 1: Start by dividing 650 by the smallest prime number, which is 2.

650 ÷ 2 = 325

Step 2: Now, we divide the quotient (325) by the smallest prime number again, which is 2.

325 ÷ 2 = 162.5

Since 162.5 is not a whole number, we move on to the next prime number, which is 3.

Step 3: Divide 325 by 3.

325 ÷ 3 = 108.33

Again, we have a decimal, so we move on to the next prime number, which is 5.

Step 4: Divide 325 by 5.

325 ÷ 5 = 65

Step 5: Divide 65 by 5.

65 ÷ 5 = 13

Step 6: Divide 13 by 5.

13 ÷ 5 = 2.6

Since 2.6 is not a whole number, we move on to the next prime number, which is 7.

Step 7: Divide 13 by 7.

13 ÷ 7 = 1.857

Again, we have a decimal, so we move on to the next prime number, which is 11.

Step 8: Divide 13 by 11.

13 ÷ 11 = 1.182

Since 1.182 is not a whole number, we move on to the next prime number, which is 13.

Step 9: Divide 13 by 13.

13 ÷ 13 = 1

Now, we have reached 1, which means we have found all the prime factors of 650.

The prime factorisation of 650 is 2 × 5 × 5 × 13.