Answer :
Final answer:
The other number is 30.
Explanation:
In number theory, the Highest Common Factor (H.C.F.) and Lowest Common Multiple (L.C.M.) of two or more integers, when multiplied together, give the product of the integers themselves. Given that the H.C.F of two numbers is 5, their L.C.M. is 150, and one of the numbers is 25, we can use this information to find the other number.
The product of the L.C.M. and H.C.F. is equal to the product of the two numbers. So with an H.C.F of 5, an L.C.M of 150, and knowing that one of the numbers is 25, we can set up the equation: 5 times 150 = 25 times the unknown number.
After simplifying the equation, we get: 750 = 25 times the unknown number. Dividing both sides of the equation by 25, we obtain the unknown number. The result is 30.
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