If n and t are positive integers, what is the greatest prime factor of the product nt ? (1) The greatest common factor of n and t is 5. (2) The least common multiple of n and t is 105.

Greatest prime factor of is 7.

Step-by-step explanation:

Given that

Two positive integers are and .

(1) Greatest Common Factor or HCF of and is 5.

(2) Least Common Multiple or LCM of and is 105.

To find:

The greatest prime factor of the product = ?

Solution:

First of all, let us learn about a property of HCF and LCM of two numbers.

The product of two numbers and is equal to the product of their HCF and LCM.

Using this property for the given numbers:

Now, let us make prime factors of to find the greatest of the prime factors.

So, the prime factors of are 5, 5, 3 and 7.

Greatest prime factor of is 7.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this