35 is a multiple of both 5 and 7 (5*7=35).

The least common multiple of 5 and 7 is 35, so any number that is a multiple of both must also be a multiple of 35.

63 is a multiple of both 7 (7x9) and 9 (9x7).

Since any multiple of 8 and 14 must also be a multiple of their GCD, which includes 2 as a factor.

The number 6 is a factor of itself and also a multiple of 6, making it the only valid option.

12 is a factor of 24 and also a multiple of 3, as 12 = 3 * 4.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Among these, 12 is a multiple of 4.

The factors of 36 that are also multiples of 6 are 6, 12, and 18. Among these, 18 is the largest.

The multiples of 4 that are also factors of 48 are 4, 8, 12, and 16. Among the options, 8 is valid.

A number congruent to 0 mod 6 must be a multiple of 6. 12 is a multiple of 6.

The number can be expressed as 11k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).

The number can be expressed as 12k + 7, where k is a non-negative integer. For k=0, the number is 7; for k=1, it is 19.

Since 7 divided by 3 gives a remainder of 1, the answer is 1.

The number can be expressed as 12k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).

23 gives a remainder of 7 when divided by 12 (12*1 + 7 = 19).

Since 7 mod 3 = 1, the remainder when the number is divided by 3 is 1.

25 gives a remainder of 10 when divided by 15 (15*1 + 10 = 25).

The remainder when the number is divided by 3 is 1, since 7 mod 3 = 1.

23 gives a remainder of 8 when divided by 15.

Since 10 is greater than 5, the remainder when 10 is divided by 5 is 0.

Since 2 is less than 3, the remainder when 2 is divided by 3 is 2.

If the number gives a remainder of 2 when divided by 6, it will give a remainder of 2 when divided by 3 as well.

The number can be expressed as 8k + 5, which gives a remainder of 1 when divided by 4.

The number can be expressed as 8k + 5. When divided by 4, the remainder is 5 mod 4 = 1.

29 gives a remainder of 2 when divided by 9 (9*3 + 2 = 29).

A number divisible by 10 is always divisible by 2 and 5, and it is also even.

A number divisible by 12 is also divisible by both 3 and 4.

A number divisible by 15 must be divisible by both 3 and 5.

A number divisible by 15 is also divisible by both 3 and 5, as 15 is the product of these two primes.

Any number divisible by 4 is even, as 4 itself is an even number.