Factorization by taking out the H.C.F The H.C.F. is an acronym stands for the Highest common Factor, this factor may be Composite or Prime. The term was revealed by the Greek scientist Euclid of Alexandria.. What if I'm saying: Find the prime factors of the composite number "180" - you start by dividing 180 by its prime factors. You divide by 2, then 2, then 3, then 3, then 5. Yes, you have found it. 180 = 2 × 2 × 3 × 3 × 5. The same thing with the composite number "240" - you start by dividing 240 by its prime factors. You divide by 2, then 2, then 2, then 2, then 3, then 5. Yes, you have found it again. 240 = 2 × 2 × 2 × 2 × 3 × 5. The new thing if tell you find the common factor of 180 and 240 together. You divide 180 by 240 to get 3 over 4 simply because you have used your previous knowledge to cancel out the similar factors between 180 and 240. The Highest common factor then is the result of multiplication of the whole similar prime factors. Here it is 60, because "3 × 60" which is actually 180 by "4 × 60" which is 240 is 3 over 4 multiplied by 60 over 60 which is actually 1, the identity element of multiplication. What if it wasn't a number, if it was an algebric term. it is the same thing like if you add 5x^2 and 15x^3. you start saying that 5x^2 is 5 multiplied by x multiplied by x. 15x^3 is 3 multiplied by 5 multiplied by x multiplied by x multiplied by x. It is clear that 5 multiplied by x multiplied by x is the highest common factor, the H.C.F. you can say that 5x^2 + 15x^3 is equal to 5x^2 multiplied by (1 + 3x) as for 5x^2 is the H.C.F. Exercises: Find the H.C.F of: I) 245 and 35 II) 30 and 42 III) 5.x.y^2 and 5.y IV) 5.x and y V) 1016.x^2.y^3 and 127.x^3.y^2 Answers: I) 35 II) 6 III) 5.y IV) No H.C.F V) 127.x^2.y^2

:ملخص للدرس من اعداد محمد البرديسى