Question

The number of commom prime factor of 70,60,105

Answer 1

70=2×5×7
60=2×2×3×5
105=3×5×7
common prime factors of 70,60 and 105 is 5

Answer 2

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$\implies$ $\textbf{For 70}$

70 divides or is divisible by the value or number "2", that is,,

$70 = 35 \times 2 \\ \\ = > 2 \times 35$

35 divides or is divisible by the value or number "5", that is,,

$35 = 7 \times 5 \\ \\ = > 2 \times 5 \times 7$

Therefore, the values or numbers, "2" , "5" , "7" , are all prime numbers or prime factors, therefore,, no further factorisation is possible.

$\implies$ $\textbf{For 60}$

60 divides or is divisible by the value or number "2" , that is,,

$60 = 3 \times 2 \\ \\ = > 2 \times 30$

30 divides or is divisible by the value or number "2" , that is,,

$30 = 15 \times 2 \\ \\ = > 2 \times 2 \times 15$

15 divides or is divisible by the value or number "3" , that is,,

$15 = 5 \times 3 \\ \\ = > 2 \times 2 \times 3 \times 5$

Therefore, the values or numbers, "2" , "3" , "5" , are all prime numbers or prime factors, therfore,, no further factorisation is possible.

$\implies$ $\textbf{For 105}$

105 divides or is divisible by the value or number "3", that is,,

$105 = 35 \times 3 \\ \\ = > 35 \times 3$

35 further divides or is divisible by the value or number "5", that is,,

$35 = 7 \times 5 \\ \\ = > 3 \times 5 \times 7$

Therefore, the values or numbers, "3" , "5" , "7" , are all prime numbers or prime factors, therefore, no further factorisation is possible.

The collective common prime factors of these three numbers is $\large\textbf{"5"}$ , since it has appeared in all three prime numbers or prime factors, hence the common or odd man out.

HOPE THIS HELPS AND CLEARS YOUR DOUBTS FOR PRIME FACTORS!!!!