Find the largest number which divides 62 132 237 to leave the same reminder
To find the largest number that divides all three numbers (62, 132, and 237) and leaves the same remainder, we need to find the greatest common divisor (GCD) of these numbers.
The prime factorization of 62 is 2 * 31.
The prime factorization of 132 is 2^2 * 3 * 11.
The prime factorization of 237 is 3 * 79.
To find the GCD, we take the common factors with the lowest exponents from the prime factorizations: 2^1 * 3^1 = 6.
Therefore, the largest number that divides 62, 132, and 237 and leaves the same remainder is 6.