**52** is divisible by 4 because 2 is an even number that is not divisible by 4, and the digit before it, 5, is an odd number. Thus 4**52** and ANY OTHER number ending in 52 is divisible by 4.

Here is another divisibility trick: 1% of all numbers end in the digits** ****52**, which is NOT divisible by 8. No matter how long the number is, if the digit immediately preceding those ending digits of **52** is odd, then that number will be divisible by 8, and if that digit is even, the number will NOT be divisible by 8. Thus 4**52** is NOT divisible by 8.

Live, Love, Laugh recently wrote a post about the Find the Factors blog. Check them out.

This Level 4 puzzle is a little tougher than usual, but if you’ve done other Level 4 puzzles, I think you can still handle it.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-04-06

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- 452 is a composite number.
- Prime factorization: 452 = 2 x 2 x 113, which can be written 452 = (2^2) x 113
- The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2 = 6. Therefore 452 has exactly 6 factors.
- Factors of 452: 1, 2, 4, 113, 226, 452
- Factor pairs: 452 = 1 x 452, 2 x 226, or 4 x 113
- Taking the factor pair with the largest square number factor, we get √452 = (√4)(√113) = 2√113 ≈ 21.2603

Since 452 has only 6 factors, we would get a two-layer cake when we use the cake method to find its factors. Dividing 452 by 4 is easier than dividing it by 2 twice, so I’ve modified the cake method to get just a one-layer cake to find the square root of 452. Since 113 is a prime number, no other divisions are possible.

To simplify the square root of 452, simply take the square root of every number on the outside of the cake. Thus √452 = (√4)(√113) = 2√113.

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Did you see the well deserved nod to your puzzles on Jo Morgan’s Resourceaholic Gem post? She wrote

“Some things are hard to categorise, but I spot them on Twitter and they capture my imagination. The winner of this category is @IvaSallay’s Find the Factors resources. I featured these in Gems 11 – they’re ‘an excellent way for children and adults to review multiplication facts, use logic, and strengthen brain power’. They are lovely puzzles”.

http://www.resourceaholic.com/2015/04/gem-awards-2015.html

Jo has good taste. 🙂

Your comment was one of the first things I saw when I came home from work. Thanks for letting me know!