Factors are the numbers that divide into another number exactly, leaving no remainder. A factor can never be greater than the original number.

To find factors efficiently:

  1. Start with $1$ and the number itself.
  2. Increment your divisor and test: Does this divide the number without a remainder?
  3. If yes, add both the divisor and its quotient.
  4. Stop when you reach or exceed the square root of the number.

Step-by-Step: Factors of 35

Start by adding the obvious factors: $$ 1, \quad 35 $$

Try 2:

$$ 35 \div 2 = 17.5 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 3:

$$ 35 \div 3 \approx 11.67 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 4:

$$ 35 \div 4 = 8.75 \quad \text{Not exact} \Rightarrow \text{Skip} $$

Try 5:

$$ 35 \div 5 = 7 \quad \text{✓ Add } 5 \text{ and } 7 $$

Updated factor list: $$ 1, \quad 5, \quad 7, \quad 35 $$

You’ve now reached $\sqrt{35} \approx 5.9$, so you can stop here.

All Factors of 35

The complete list of factors: $$ 1, \quad 5, \quad 7, \quad 35 $$

Because there are more than two factors, $35$ is a composite number.

✅ The highest factor other than $35$ is: $$ \boxed{7} $$

Summary

  • A factor is a number that divides exactly into another number.
  • The factors of $35$ are: $$ 1, \quad 5, \quad 7, \quad 35 $$
  • Since it has more than two factors, $35$ is a composite number — not prime.