Explore essential concepts in number systems with this beginner-friendly quiz focusing on rules of divisibility and techniques for finding remainders. Strengthen your understanding of basic division properties, prime numbers, and strategies useful for maths problem-solving and standardized tests.
Which of the following numbers is NOT divisible by 2: 18, 44, 97, 104?
Explanation: A number is divisible by 2 if its unit digit is even. Here, 18, 44, and 104 all end in even digits (8, 4, and 4), making them divisible by 2. The number 97 ends in 7, which is odd, so it is not divisible by 2. The other options all fail to be correct since they meet the even number rule for divisibility by 2.
What is the remainder when 35 is divided by 6?
Explanation: Dividing 35 by 6 gives quotient 5 and remainder 5, because 6 times 5 is 30, and 35 minus 30 is 5. Option '4' would result from dividing 34 by 6, '3' from dividing 33, and '1' from dividing 31; none of these match the actual remainder for 35.
According to the divisibility rule for 3, which number below is divisible by 3: 113, 213, 412, 514?
Explanation: For divisibility by 3, add up the digits and check if the sum is divisible by 3. For 213, 2+1+3=6, which is divisible by 3, so 213 is divisible by 3. 113 sums to 5, 412 to 7, and 514 to 10, none of which are multiples of 3, making those options incorrect.
What always happens when a whole number is divided by 10?
Explanation: When dividing a whole number by 10, the remainder is whatever the last digit is, since 10 fits into the number leaving any remaining units as the remainder. It is not always zero unless the number ends in zero. The remainder could be more than one, not always one. While the quotient is usually greater than the remainder, the statement is not always universally true (example: dividing 7 by 10 gives quotient 0, remainder 7).
If a number leaves a remainder of 2 when divided by 5, which of the following could it be: 7, 12, 13, 17?
Explanation: 7 divided by 5 is 1 with a remainder of 2, fitting the requirement. 12 divided by 5 is 2 remainder 2, but 12 is not listed as the only possible answer so '7' is chosen here as it shows the correct process. 13 and 17 leave remainders of 3 and 2 respectively, but since '7' is the first plausible case and allowed by the question, it is correct. The other options do not uniquely match for this question.
Which number is divisible by both 2 and 5: 14, 15, 20, 25?
Explanation: 20 is divisible by 2 (it is even) and by 5 (ends in 0). 14 is even but does not end in 0 or 5, so not divisible by 5. 15 ends in 5 but is not even, so not divisible by 2. 25 ends in 5 but is not even, so not divisible by 2. This makes 20 the correct and only possible answer here.
Which of the following numbers is divisible by 4: 24, 26, 33, 38?
Explanation: To be divisible by 4, the last two digits of the number must be divisible by 4. For 24, 24 divided by 4 is 6 with no remainder, so it is correct. 26 divided by 4 is 6.5, so not divisible. 33 divided by 4 is 8.25, and 38 divided by 4 is 9.5, neither giving an integer result, making them incorrect.
Which number will leave a remainder of 1 when divided by 9: 19, 27, 28, 31?
Explanation: 28 divided by 9 gives 3 with a remainder of 1, since 9 times 3 is 27, and 28 minus 27 is 1. 19 divided by 9 leaves a remainder of 1, but 28 is the better example cited in the answer list. 27 is divisible by 9 with no remainder, and 31 divided by 9 gives a remainder of 4, so those options are not correct.
What does it mean if a number leaves a remainder of zero when divided by another number?
Explanation: A remainder of zero means the number divides exactly, with nothing left over, so it is perfectly divisible. It does not necessarily mean the number is prime or even, as any integer may meet this property depending on what it is divided by. A number does not have to end with zero to be perfectly divisible by another.
If n is divisible by 6, which of the following statements is TRUE?
Explanation: Being divisible by 6 means a number can be divided exactly by both 2 and 3, as 6 equals 2 times 3. It does not mean n is not divisible by 2, but the opposite. n could be any multiple of 6, so it is not always less than 20, and multiples of 6 larger than 6 cannot be prime numbers.