A question of prime factors... The answer is 2 x 2 x 3 x 5 x 7 = 420 2 x 2 x 3 x 5 x 7 gives us a factor of 2... 2 x 2 x 3 x 5 x 7 and of 3... 2 x 2 x 3 x 5 x 7 and of 4... 2 x 2 x 3 x 5 x 7 and of 5... 2 x 2 x 3 x 5 x 7 and of 6... 2 x 2 x 3 x 5 x 7 and of 7.
2 x 3 x 7 x 25 5 x 5 x 6 x 7 3 x 5 x 7 x 10 3 x 5 x 5 x 14 2 x 5 x 7 x 15 2 x 5 x 5 x 21 2 x 3 x 5 x 35
105. 525 = 3 x 52 x 7 210 = 2 x 3 x 5 x 7 gcf = 3 x 5 x 7 = 105
Count the number of times each digit appears in the multiplication and then write each digit once in the multiplication with the number of times they originally appeared as an index (little superscript number): 3 appears 2 times 5 appears 4 times 7 appears 1 times → 3 x 3 x 5 x 5 x 5 x 5 x 7 = 32 x 54 x 71 However, when the index is 1, it is not normally written, so this becomes: 3 x 3 x 5 x 5 x 5 x 5 x 7 = 32 x 54 x 7
Factor them. 2 x 3 x 5 x 5 x 7 = 1050 5 x 5 x 7 x 7 = 1225 Select the common factors. 5 x 5 x 7 = 175, the GCF
Prime factors are 3, 3, 5, 5, 7 Others are combinations of the prime factors, i.e. 3 x 3 = 9 3 x 5 = 15 3 x 7 = 21 5 x 5 = 25 5 x 7 = 35 3 x 3 x 5 = 45 3 x 3 x 7 = 63 3 x 5 x 5 = 75 3 x 5 x 7 = 105 5 x 5 x 7 = 175 3 x 3 x 5 x 5 = 225 3 x 3 x 5 x 7 = 315 3 x 5 x 5 x 7 = 525
A question of prime factors... The answer is 2 x 2 x 3 x 5 x 7 = 420 2 x 2 x 3 x 5 x 7 gives us a factor of 2... 2 x 2 x 3 x 5 x 7 and of 3... 2 x 2 x 3 x 5 x 7 and of 4... 2 x 2 x 3 x 5 x 7 and of 5... 2 x 2 x 3 x 5 x 7 and of 6... 2 x 2 x 3 x 5 x 7 and of 7.
1575 = 3 x 3 x 5 x 5 x 7 = 32 x 52 x 7
3 x 175 5 x 105 7 x 75 15 x 35 21 x 25 3 x 5 x 35 3 x 7 x 25 5 x 7 x 15 5 x 5 x 21 3 x 5 x 5 x 7
3^3 x 5^2 x 7
2 x 3 x 7 x 25 2 x 5 x 7 x 15 5 x 5 x 6 x 7 3 x 5 x 5 x 14 3 x 5 x 7 x 10 2 x 5 x 5 x 21 2 x 3 x 5 x 35
The prime factors of 525 are: 3 x 5 x 5 x 7
3 x 5 x 5 x 7
2 x 3 x 7 x 25 5 x 5 x 6 x 7 3 x 5 x 7 x 10 3 x 5 x 5 x 14 2 x 5 x 7 x 15 2 x 5 x 5 x 21 2 x 3 x 5 x 35
105 = 3 x 5 x 7441 = 3 x 3 x 7 x 7The LCM is the lowest number that has all of the factors of each of the given numbers (each, not all), so...LCM = 3 x 3 x 5 x 7 x 7 = 2205
35 = 5 x 7 105 = 5 x 7 x 3 175 = 5 x 7 x 5 gcf = 5 x 7 x 3 x 5 = 105 x 5 = 525
2 x 3 = 6 2 x 5 = 10 2 x 7 = 14 3 x 5 = 15 3 x 7 = 21 2 x 3 x 5 = 30 5 x 7 = 35 2 x 3 x 7 = 42 3 x 5 x 7 = 105 2 x 3 x 5 x 7 = 210