Factors are the numbers that divide evenly into another number without leaving a remainder. A factor is never larger than the original number.

To find factors quickly:

  1. Start at $1$ (since $1$ divides every integer).
  2. Incrementally test whether each number divides the original number exactly.
  3. If it does, add both the divisor and the quotient.
  4. Stop once your divisor exceeds or reaches the square root of the number.

Step-by-Step: Factors of 49

Start your working list with: $$ 1, \quad 49 $$

Try 2:

$$ 49 \div 2 = 24.5 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 3:

$$ 49 \div 3 \approx 16.33 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 4:

$$ 49 \div 4 = 12.25 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 5:

$$ 49 \div 5 = 9.8 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 6:

$$ 49 \div 6 \approx 8.167 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Now try: $$ 49 \div 7 = 7 \quad \Rightarrow \text{Add } 7 $$

Now that you’ve reached $\sqrt{49} = 7$, you can stop.

All Factors of 49

You now have the full list of factors: $$ 1, \quad 7, \quad 49 $$

Since $49$ has more than two factors, it is a composite number.

✅ The highest factor other than $49$ itself is: $$ \boxed{7} $$

Summary

  • Factors are numbers that divide another number exactly.
  • The factors of $49$ are: $$ 1, \quad 7, \quad 49 $$
  • Because it has more than two factors, $49$ is a composite number (not prime).