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Division Ladders are useful for finding Greatest Common Factors, also known as Greatest Common Divisors. If your math problem is Find the GCF of 32, 24, and 40 using a Division Ladder, you would find the answer thusly:

2 |32, 24, 40

, |_________

2 |16, 12, 20

, |________

2 | 8, 6, 10

, |_________

, 4, 3, 5

You would be dividing by 2 in this case, then multiply your divisors, 2x2x2 = 8. Your Greatest Common Factor for 32, 24, and 40 is 8. I used the commas for placeholders, as without them, the vertical lines don't line up.

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Q: What is an example of a division ladder?
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when you need to get it down to a prime number


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What is a division ladder?

A division ladder is a method of finding the prime factors of a number. The number is divided by a prime number. That result is divided by another prime number. This continues until the result itself is a prime number. This result and the divisor from each step are the prime factors of the number. Here are the steps, but not quite the appearance of the division ladder. 108 ÷ 2 = 54 ÷ 2 = 27 ÷ 3 = 9 ÷ 3 = 3 The prime factors of 108 are 2, 2, 3, 3, and 3. Here is an example that better replicates the appearance of a division ladder that goes downward. 2 | 168 ...----- ..2 | 84 .....---- ..2 | 42 .....---- ..3 | 21 .....---- .........7 The prime factors of 168 are 2, 2, 2, 3, and 7.