395 ends with a five so it is a composite number that is divisible by 5.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-02-16

• 395 is a composite number.
• Prime factorization: 395 = 5 x 79
• 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 395 has exactly 4 factors.
• Factors of 395: 1, 5, 79, 395
• Factor pairs: 395 = 1 x 395 or 5 x 79
• 395 has no square factors that allow its square root to be simplified. √395 ≈ 19.875

Since 394 is an even number not divisible by 4, it can’t be part of a primitive Pythagorean triple. Scroll down past the puzzle to see its factors and its two non-primitive triples.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-02-16

• 394 is a composite number.
• Prime factorization: 394 = 2 x 197
• 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 394 has exactly 4 factors.
• Factors of 394: 1, 2, 197, 394
• Factor pairs: 394 = 1 x 394 or 2 x 197
• 394 has no square factors that allow its square root to be simplified. √394 ≈ 19.849

To find Pythagorean triples with the number 394, first divide it in half to get 197. Since 197 is 14² + 1, we know it is the hypotenuse of the triple formed from 2(14 x 1), 14² – 1, and 14² + 1 or (28-195-197). If we multiply that triple by 2, we get (56-390-394).

Prime number 197 is also the short leg of the primitive Pythagorean triple, (197-19404-19405). Doubling each element of that triple gives us (394-38808-38810).

392 is divisible by seven because 39 minus two times the last digit is 35, a multiple of seven. That is one of the reasons 392 is a composite number. All of its factors are listed below the puzzle.

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

• 392 is a composite number.
• Prime factorization: 392 = 2 x 2 x 2 x 7 x 7, which can be written 392 = (2^3) x (7^2)
• The exponents in the prime factorization are 3 and 2. Adding one to each and multiplying we get (3 + 1)(2 + 1) = 4 x 3 = 12. Therefore 392 has exactly 12 factors.
• Factors of 392: 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
• Factor pairs: 392 = 1 x 392, 2 x 196, 4 x 98, 7 x 56, 8 x 49, or 14 x 28
• Taking the factor pair with the largest square number factor, we get √392 = (√2)(√196) = 14√2 ≈ 19.799

2^391 (mod 391) = 179, not 2 so 391 is definitely a composite number. Scroll down below the puzzle to view its factors.

When I was in elementary school, my sister, Sue, taught me a song she learned in her junior high choir class. I’m not able to find these lyrics on the internet, but as best as I can remember, the words of the song were:

In the woods, in the spring, blooms the lovely wild rose. Every bud waking facing the sun. Hearts of spring, beat on thee, as the light of day grows. Dew drops glisten on you, Wild Rose. Fill the countryside with your lovely fragrance. Sun keeps your petals warm, leaves hide you from harm. Day will break, petals close, close them, oh, so tightly. Cover your beauty from the cool night. Birds, winging, singing through the woodland. Sleep and dream, sleep and dream, sleep and dream.

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

• 391 is a composite number.
• Prime factorization: 391 = 17 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 391 has exactly 4 factors.
• Factors of 391: 1, 17, 23, 391
• Factor pairs: 391 = 1 x 391 or 17 x 23
• 391 has no square factors that allow its square root to be simplified. √391 ≈ 19.774

• Note that 17 + 3 = 20, and 20 + 3 = 23, and (20^2) – (3^2) = 400 – 9 = 391.
• 2(3*20), (20^2) – (3^2), (20^2) + (3^2) makes primitive Pythagorean triple 120-391-409.
• 391-76440-76441 is another primitive Pythagorean triple
• 184-345-391 is [8-15-17] multiplied by 23
• 391-3312-3335 is [17-144-145] multiplied by 23
• 391-4488-4505 is [23-264-265] multiplied by 17

391 is in this cool pattern:

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

88 is divisible by 4 so 388 is also divisible by 4 and is a composite number. 88 is also divisible by 8, but the third to the last digit is odd, making 388 NOT divisible by 8.

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

• 388 is a composite number.
• Prime factorization: 388 = 2 x 2 x 97, which can be written 388 = (2^2) x 97
• 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 388 has exactly 6 factors.
• Factors of 388: 1, 2, 4, 97, 194, 388
• Factor pairs: 388 = 1 x 388, 2 x 194, or 4 x 97
• Taking the factor pair with the largest square number factor, we get √388 = (√4)(√97) = 2√97 ≈ 19.698

A Logical Approach to FIND THE FACTORS: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.

Is 387 prime or composite? Well, 8 + 7 = 15, a multiple of 3, so 387 is a composite number divisible by 3.

Here’s sending a little luv your way!

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

• 387 is a composite number.
• Prime factorization: 387 = 3 x 3 x 43, which can be written 387 = (3^2) x 43
• 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 387 has exactly 6 factors.
• Factors of 387: 1, 3, 9, 43, 129, 387
• Factor pairs: 387 = 1 x 387, 3 x 129, or 9 x 43
• Taking the factor pair with the largest square number factor, we get √387 = (√9)(√43) = 3√43 ≈ 19.672

386 is even and composite.

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

• 386 is a composite number.
• Prime factorization: 386 = 2 x 193
• 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 386 has exactly 4 factors.
• Factors of 386: 1, 2, 193, 386
• Factor pairs: 386 = 1 x 386 or 2 x 193
• 386 has no square factors that allow its square root to be simplified. √386 ≈ 19.647