Q4 Use prime factors to find the highest number that will divide into both 93 and 155.

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To find the highest number that will divide both 93 and 155, we need to determine the greatest common divisor (GCD) using prime factorization. Let's follow these steps:

1. **Find the prime factors of 93:**
   - 93 is an odd number, so it is not divisible by 2.
   - The sum of the digits of 93 is $$9 + 3 = 12$$, which is divisible by 3. Therefore, 93 is divisible by 3.
   - Dividing, we get $$93 \div 3 = 31$$.
   - Now, we check if 31 is a prime number. It is not divisible by any prime numbers less than its square root (which is approximately 5.57), so 31 is prime.

Thus, the prime factorization of 93 is:
   $$
   93 = 3 \times 31
   $$

2. **Find the prime factors of 155:**
   - 155 is also an odd number, so it is not divisible by 2.
   - The sum of the digits of 155 is $$1 + 5 + 5 = 11$$, which is not divisible by 3.
   - 155 ends in 5, so it is divisible by 5. Dividing, we get $$155 \div 5 = 31$$.
   - We already know that 31 is a prime number.

Thus, the prime factorization of 155 is:
   $$
   155 = 5 \times 31
   $$

3. **Identify the common prime factors:**
   - The prime factors of 93 are $$3$$ and $$31$$.
   - The prime factors of 155 are $$5$$ and $$31$$.
   - The common prime factor is $$31$$.

4. **Conclusion:**
   - The highest number that will divide both 93 and 155 is $$31$$.

Therefore, the answer is:
$$
\text{GCD}(93, 155) = 31
$$
The highest number that divides both 93 and 155 is 31.

Q4 Use prime factors to find the highest number that will divide into both 93 and 155.

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