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# How do you find the prime factorization of 78?

1. starting with the first Prime number (2), setting the result to 78
2. check if the current result is divisible by the current prime
3. if it does not divide repeat from step 2 with the next prime number
4. make a note of the prime number
5. divide the current result by the current prime number and make the result the current result
6. if current result is not 1 repeat from step 2
7. The list of primes noted in step 4 form the prime factorisation.

1. current prime = 2, current result = 78

2. 78 is divisible by 2

3. current result is divisible

4. Note: 2

5. 78 ÷ 2 = 39 → current result

6. current result not 1, repeat from step 2

2. 39 is not divisible by 2

3. set current prime to 3, repeat from step 2

2. 39 is divisible by 3

3. current result is divisible

4. Note: 3

5. 39 ÷ 3 = 13 → current result

6. current result not 1, repeat from 2

2. 13 not divisible by 3

3. next prime (5) → current prime

2. 13 not divisible by 5

3. next prime (7) → current prime

2. 13 not divisible by 7

3. next prime (11) → current prime

2. 13 not divisible by 11

3. next prime (13) → current prime

2. 13 divisible by 13

3. current result is divisible

4. Note: 13

5. 13 ÷ 13 = 1 → current result

6. current result is 1

7. factorisation of 78 is 2 x 3 x 13.

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