Finding the Highest Common Factor of 3-Digit Numbers Activity Sheet - Free Printable

I need to find the highest common factor (HCF) of 240 and 250.

Let me work through this step by step using both methods shown in the worksheet.

Method 1: Finding all factors

First, let me find all the factors of 240:
- 240 ÷ 1 = 240 ✓
- 240 ÷ 2 = 120 ✓
- 240 ÷ 3 = 80 ✓
- 240 ÷ 4 = 60 ✓
- 240 ÷ 5 = 48 ✓
- 240 ÷ 6 = 40 ✓
- 240 ÷ 8 = 30 ✓
- 240 ÷ 10 = 24 ✓
- 240 ÷ 12 = 20 ✓
- 240 ÷ 15 = 16 ✓
- 240 ÷ 16 = 15 ✓
- 240 20 = 12 ✓
- 240 ÷ 24 = 10 ✓
- 240 ÷ 30 = 8 ✓
- 240 ÷ 40 = 6 ✓
- 240 ÷ 48 = 5 ✓
- 240 ÷ 60 = 4 ✓
- 240 80 = 3 ✓
- 240 ÷ 120 = 2 ✓
- 240 ÷ 240 = 1 ✓

Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

Now, let me find all the factors of 250:
- 250 ÷ 1 = 250 ✓
- 250 ÷ 2 = 125 ✓
- 250 ÷ 5 = 50 ✓
- 250 ÷ 10 = 25 ✓
- 250 ÷ 25 = 10 ✓
- 250 ÷ 50 = 5 ✓
- 250 ÷ 125 = 2 ✓
- 250 ÷ 250 = 1 ✓

Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250

Now I need to find which numbers appear in BOTH lists:
Common factors: 1, 2, 5, 10

The highest common factor is 10.

Method 2: Using prime factorization

Let me verify using prime factors:

Prime factorization of 240:
240 = 2 × 120
= 2 × 2 × 60
= 2 × 2 × 2 × 30
= 2 × 2 × 2 × 2 × 15
= 2 × 2 × 2 × 2 × 3 × 5

So 240 = 2 × 3 × 5

Prime factorization of 250:
250 = 2 × 125
= 2 × 5 × 25
= 2 × 5 × 5 × 5
= 2 × 5³

So 250 = 2 × 5³

To find the HCF, I take the lowest power of each common prime factor:
- For 2: min(2⁴, 2¹) = 2¹ = 2
- For 5: min(5¹, 5³) = 5¹ = 5
- For 3: only appears in 240, so not included

HCF = 2 × 5 = 10

Both methods give the same answer!

Final Answer: 10