Final answer:
To find the number when 120, 134, and 162 are divided by it and the remainder is always 1, we can use the concept of congruences.
Step-by-step explanation:
To find the number when 120, 134, and 162 are divided by it and the remainder is always 1, we can use the concept of congruences. Let's assume the number is x. So, the congruences can be written as:
120 ≡ 1 (mod x)
134 ≡ 1 (mod x)
162 ≡ 1 (mod x)
From these congruences, we can conclude that x-1 divides 120-1, 134-1, and 162-1 without any remainder. Therefore, we can find the number x by finding the greatest common divisor of 119, 133, and 161. After calculating, we find that the greatest common divisor of these numbers is 7. Hence, the number is 7.