Subjects number theory

Prime Factors Ages 46123C

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Question: User: 67 46 52 67 99 composite composite odd number composite Do as indicated. Pablo and Sebastian are brothers. Pablo's age is the sum of all the factors used in the prime factorization of 99. Sebastian's age is the sum of all the factors used in the prime factorization of 88. How old are Pablo and Sebastian? The numbers 3 and 5 are called twin primes; they differ by 2. Other twin primes are 5 and 7. Give some pairs of twin primes.
1. **State the problem:** We need to find Pablo's and Sebastian's ages based on the sum of the prime factors of 99 and 88 respectively. 2. **Prime factorization:** - For Pablo: Find prime factors of $$99$$. - For Sebastian: Find prime factors of $$88$$. 3. **Prime factorization of $$99$$:** $$99 = 3 \times 3 \times 11$$ The factors used are $$3, 3, 11$$. 4. **Sum of factors for Pablo:** $$3 + 3 + 11 = 17$$ So, Pablo is $$17$$ years old. 5. **Prime factorization of $$88$$:** $$88 = 2 \times 2 \times 2 \times 11$$ The factors used are $$2, 2, 2, 11$$. 6. **Sum of factors for Sebastian:** $$2 + 2 + 2 + 11 = 17$$ So, Sebastian is also $$17$$ years old. **Final answer:** Pablo is 17 years old and Sebastian is 17 years old.