If a number is divisible by 63, then which among the following numbers also…

To determine which number must also divide a number that is already divisible by 63, we rely on the fundamental property of divisibility: if a number is divisible by a value, it is also divisible by all the factors of that value.

Step-by-Step Solution

1. Understand the Divisibility Rule: If a number N is divisible by D, then N is also divisible by every factor of D.

2. Factorize 63: To find the factors of 63, we perform prime factorization:

   • 63 = 9 * 7

   • 63 = 3 * 3 * 7

   • The factors of 63 are 1, 3, 7, 9, 21, and 63.

3. Analyze the Requirement: We are looking for a number that must divide any multiple of 63. Based on the rule, any factor of 63 will satisfy this.

   • 3 is a factor of 63.

   • 7 is a factor of 63.

   • Therefore, both 3 and 7 must divide any number divisible by 63.