In a month my husband and I will celebrate our 38th wedding anniversary. David Mitchell has given us an early and lovely present, wedding anniversary tessellations. Tessellations are quite fascinating and the ones he makes are very intricate and well worth a look.

The Factors of 437 are listed below the puzzle.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-03-23

• 437 is a composite number.
• Prime factorization: 437 = 19 x 23
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 437 has exactly 4 factors.
• Factors of 437: 1, 19, 23, 437
• Factor pairs: 437 = 1 x 437 or 19 x 23
• 437 has no square factors that allow its square root to be simplified. √437 ≈ 20.9045

The factors of 430 are listed after the puzzle.

What interesting fact could I say about the number 430? I did a little research.

Biblewheel.com quotes a verse from Galatians 3:17 in the Bible: “And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect.” Biblewheel states that 430 means the law, just as 666 means the beast.

OEIS.org says that 430 “is the number of necklaces possible with 6 beads, each being one of 4 colors.” If I understood what that means in English, I’m sure I could construct it mathematically. I know it can’t mean 6 Choose 4. If you understand what it means, please comment.

Print the puzzles or type the factors on this excel file:10 Factors 2015-03-16

• 430 is a composite number.
• Prime factorization: 430 = 2 x 5 x 43
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 430 has exactly 8 factors.
• Factors of 430: 1, 2, 5, 10, 43, 86, 215, 430
• Factor pairs: 430 = 1 x 430, 2 x 215, 5 x 86, or 10 x 43
• 430 has no square factors that allow its square root to be simplified. √430 ≈ 20.7364

415 is obviously a multiple of 5 so it is a composite number. Scroll down past the puzzle to view its other factors.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-03-02

• 415 is a composite number.
• Prime factorization: 415 = 5 x 83
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 415 has exactly 4 factors.
• Factors of 415: 1, 5, 83, 415
• Factor pairs: 415 = 1 x 415 or 5 x 83
• 415 has no square factors that allow its square root to be simplified. √415 ≈ 20.3715

Let’s apply the 7 divisibility trick to 406.

• Separate the last digit from the rest and multiply that last digit by two: 6 x 2 = 12.
• Now find the difference between the remaining number, 40 and 12: 40 – 12 = 28.
• Since 28 is a multiple of 7, we know that 406 is also divisible by 7.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-02-23

• 406 is a composite number.
• Prime factorization: 406 = 2 x 7 x 29
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 406 has exactly 8 factors.
• Factors of 406: 1, 2, 7, 14, 29, 58, 203, 406
• Factor pairs: 406 = 1 x 406, 2 x 203, 7 x 58, or 14 x 29
• 406 has no square factors that allow its square root to be simplified. √406 ≈ 20.1494

390 is a multiple of 6 because it is even and all of its digits are divisible by 3. Scroll down past the puzzle to view its factors.

Print the puzzles or type the factors on this excel file:12 Factors 2015-02-09

• 390 is a composite number.
• Prime factorization: 390 = 2 x 3 x 5 x 13
• The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 x 2 = 16. Therefore 390 has exactly 16 factors.
• Factors of 390: 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
• Factor pairs: 390 = 1 x 390, 2 x 195, 3 x 130, 5 x 78, 6 x 65, 10 x 39, 13 x 30, or 15 x 26
• 390 has no square factors that allow its square root to be simplified. √390 ≈ 19.748

Is 381 Prime or composite? Its digits can be grouped into 3 and 81. Both groups are divisible by 3 so 381 is composite. Scroll down past the puzzle to view its factors.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-02-02

• 381 is a composite number.
• Prime factorization: 381 = 3 x 127
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 381 has exactly 4 factors.
• Factors of 381: 1, 3, 127, 381
• Factor pairs: 381 = 1 x 381 or 3 x 127
• 381 has no square factors that allow its square root to be simplified. √381 ≈ 19.519

Pythagorean triples:

• 381 – 508 – 635 which is 127 times (3 – 4 – 5 )
• 381 – 24192 – 24195 which is 3 times (127 – 8064 – 8065)
• 381 – 8060 – 8069, a primitive
• 381 – 72580 – 72581, a primitive

372 is even and therefore a composite number. Scroll down for its factoring information.

Print the puzzles or type the factors on this excel file:12 Factors 2015-01-26

• 372 is a composite number.
• Prime factorization: 372 = 2 x 2 x 3 x 31, which can be written 372 = (2^2) x 3 x 31
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 372 has exactly 12 factors.
• Factors of 372: 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372
• Factor pairs: 372 = 1 x 372, 2 x 186, 3 x 124, 4 x 93, 6 x 62, or 12 x 31
• Taking the factor pair with the largest square number factor, we get √372 = (√4)(√93) = 2√93 ≈ 19.287

Every digit of 363 is divisible by 3, so 363 is divisible by 3 and is a composite number. Its factor information is given below the puzzle.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-01-19

• 363 is a composite number.
• Prime factorization: 363 = 3 x 11 x 11, which can be written 363 = 3 x (11^2)
• The exponents in the prime factorization are 1 and 2. Adding one to each and multiplying we get (1 + 1)(2 + 1) = 2 x 3  = 6. Therefore 363 has exactly 6 factors.
• Factors of 363: 1, 3, 11, 33, 121, 363
• Factor pairs: 363 = 1 x 363, 3 x 121, or 11 x 33
• Taking the factor pair with the largest square number factor, we get √363 = (√3)(√121) = 11√3 ≈ 19.053