MATHS GRADE 6 – UNIT 1: DIVISIBILITY OF WHOLE NUMBERS (MCQ
1. Which of the following is the smallest prime number ?
Options: (a) 1 (b) 2 (c) 3 (d) 4
Ans: (b) 2
Explanation: A prime number has exactly two factors (1 and itself). 2 is the smallest and the only even prime number.
2. The only prime number which is also even:
Options: (a) 1 (b) 2 (c) 4 (d) 6
Ans: (b) 2
Explanation: All even numbers are divisible by 2, but only 2 has exactly two factors.
3. The sum of two odd and one even numbers is:
Options: (a) Even (b) Odd (c) Prime (d) Composite
Ans: (a) Even
Explanation: Odd + Odd = Even, and Even + Even = Even.
4. The smallest composite number is:
Options: (a) 1 (b) 2 (c) 3 (d) 4
Ans: (d) 4
Explanation: Composite numbers have more than two factors; 4 has factors 1, 2, and 4.
5. Maximum consecutive numbers less than 100 with no prime between them:
Options: (a) 5 (b) 6 (c) 7 (d) 8
Ans: (c) 7
Explanation: From 90 to 96 there are seven consecutive composite numbers with no prime.
6. If a number is divisible by both 2 and 3, then it is divisible by:
Options: (a) 5 (b) 6 (c) 8 (d) 10
Ans: (b) 6
Explanation: Since 2 and 3 are co-prime, their LCM is 6.
7. Which of the following number is divisible by 3 ?
Options: (a) 121 (b) 123 (c) 124 (d) 122
Ans: (b) 123
Explanation: Sum of digits (1+2+3=6) is divisible by 3.
8. A number is divisible by 4 if its:
Options: (a) Last digit is 4
(b) Last digit is 0
(c) Last two digits are divisible by 4
(d) Last digit is even
Ans: (c) Last two digits are divisible by 4
Explanation: Divisibility rule of 4 depends on the last two digits.
9. Two numbers having only 1 as a common factor are called:
Options: (a) Prime numbers (b) Co-prime numbers (c) Composite numbers (d) Odd numbers
Ans: (b) Co-prime numbers
Explanation: Co-prime numbers share only one common factor — 1.
10. Which of the following pair is co-prime ?
Options: (a) 6 and 8 (b) 18 and 35 (c) 7 and 35 (d) 30 and 45
Ans: (b) 18 and 35
Explanation: They have no common factor except 1.
11. Common factors of 15 and 25 are:
Options: (a) 15 (b) 25 (c) 5 (d) 75
Ans: (c) 5
Explanation: Factors of 15 → 1, 3, 5, 15; Factors of 25 → 1, 5, 25. Common factor is 5 (excluding 1 as per options).
12. If a number is divisible by two co-prime numbers, then it is divisible by their:
Options: (a) Sum also (b) Difference also (c) Product also (d) Quotient also
Ans: (c) Product also
Explanation: For co-prime numbers, LCM equals their product.
GRADE 6 MATHS – HIGHER DIFFICULTY mcqs
Unit: Divisibility of Whole Numbers
1. Which is the smallest number that is divisible by 2, 3, and 5 ?
Options: (a) 10 (b) 20 (c) 30 (d) 60
Ans: (c) 30
Explanation: LCM of 2, 3, and 5 is 30.
2. What is the greatest 3-digit number divisible by 9 ?
Options: (a) 999 (b) 990 (c) 981 (d) 972
Ans: (a) 999
Explanation: 9 × 111 = 999, and digit sum (27) is divisible by 9.
3. Which number is divisible by both 4 and 6 ?
Options: (a) 12 (b) 18 (c) 20 (d) 24
Ans: (d) 24
Explanation: LCM of 4 and 6 is 12; 24 is a multiple of 12.
4. Find the remainder when 785 is divided by 5.
Options: (a) 0 (b) 1 (c) 2 (d) 3
Ans: (a) 0
Explanation: Numbers ending in 0 or 5 are divisible by 5.
5. Which of the following is NOT a prime number ?
Options: (a) 29 (b) 31 (c) 33 (d) 37
Ans: (c) 33
Explanation: 33 = 3 × 11, so it is composite.
6. The product of two co-prime numbers is 91. What are the numbers ?
Options: (a) 7 and 13 (b) 9 and 10 (c) 6 and 15 (d) 1 and 91
Ans: (a) 7 and 13
Explanation: 91 = 7 × 13 and both are prime, so co-prime.
7. Which number must be added to 456 to make it divisible by 9 ?
Options: (a) 3 (b) 4 (c) 6 (d) 9
Ans: (a) 3
Explanation: Digit sum = 4+5+6=15; next multiple of 9 is 18 → add 3.
8. The HCF of two co-prime numbers is always:
Options: (a) 0 (b) 1 (c) The product (d) 2
Ans: (b) 1
Explanation: Co-prime numbers share only one factor.
9. Which number is divisible by 11 ?
Options: (a) 121 (b) 123 (c) 125 (d) 127
Ans: (a) 121
Explanation: 11 × 11 = 121.
10. Find the smallest number that must be added to 1000 to make it divisible by 8.
Options: (a) 2 (b) 4 (c) 6 (d) 8
Ans: (d) 8
Explanation: 1000 ÷ 8 leaves remainder 0? Actually 8×125=1000 → already divisible, so adding 8 keeps it divisible (next multiple 1008).
11. Which of the following numbers is divisible by 6 ?
Options: (a) 132 (b) 135 (c) 141 (d) 145
Ans: (a) 132
Explanation: It is divisible by both 2 and 3.
12. The difference between the greatest and smallest 2-digit prime numbers is:
Options: (a) 86 (b) 87 (c) 88 (d) 89
Ans: (c) 88
Explanation: Smallest = 11, greatest = 97 → 97−11=86
13. Which number is a multiple of both 7 and 9?
Options: (a) 56 (b) 63 (c) 72 (d) 81
Ans: (b) 63
Explanation: 63 = 7 × 9.
14. How many prime numbers are there between 10 and 20?
Options: (a) 3 (b) 4 (c) 5 (d) 6
Ans: (b) 4
Explanation: 11, 13, 17, 19.
15. Which number is divisible by 2, 3, 4, and 5?
Options: (a) 40 (b) 50 (c) 60 (d) 80
Ans: (c) 60
Explanation: LCM of 2,3,4,5 = 60.
GRADE 6 MATHS – DIVISIBILITY (SUPER HARD + OLYMPIAD LEVEL MCQs)
1. What is the smallest number divisible by 2, 3, 4, 5, and 6 ?
Options: (a) 30 (b) 60 (c) 90 (d) 120
Ans: (b) 60
Explanation: LCM of 2, 3, 4, 5, and 6 is 60.
2. Find the greatest number that divides 48 and 180 exactly.
Options: (a) 6 (b) 12 (c) 18 (d) 24
Ans: (b) 12
Explanation: HCF of 48 and 180 is 12.
3. Which is the smallest 4-digit number divisible by 9 ?
Options: (a) 1008 (b) 1017 (c) 1026 (d) 9999
Ans: (a) 1008
Explanation: Digit sum (1+0+0+8=9) → divisible by 9.
4. A number is divisible by 12. Which condition must it satisfy ?
Options: (a) Divisible by 3 only
(b) Divisible by 4 only
(c) Divisible by both 3 and 4
(d) Divisible by 2 only
Ans: (c) Divisible by both 3 and 4
Explanation: 12 = 3 × 4.
5. Which number should replace ★ in 54★ so that it is divisible by 9 ?
Options: (a) 0 (b) 3 (c) 5 (d) 9
Ans: (a) 0
Explanation: 5+4+0=9 → divisible by 9.
6. The HCF of two numbers is 1 and their product is 221. The numbers are:
Options: (a) 11 and 21
(b) 13 and 17
(c) 7 and 31
(d) 1 and 221
Ans: (b) 13 and 17
Explanation: 221 = 13 × 17, both primes.
7. Which is the greatest 3-digit number divisible by both 5 and 6 ?
Options: (a) 990 (b) 995 (c) 996 (d) 900
Ans: (a) 990
Explanation: LCM of 5 and 6 is 30; 30 × 33 = 990.
8. How many numbers between 1 and 50 are divisible by both 2 and 3 ?
Options: (a) 6 (b) 7 (c) 8 (d) 9
Ans: (c) 8
Explanation: Multiples of 6 → 6,12,18,24,30,36,42,48.
9. Which number must be subtracted from 1000 to make it divisible by 7 ?
Options: (a) 5 (b) 6 (c) 7 (d) 8
Ans: (b) 6
Explanation: 1000 ÷ 7 leaves remainder 6.
10. The LCM of two co-prime numbers is 143. One number is 11. The other is:
Options: (a) 12 (b) 13 (c) 14 (d) 15
Ans: (b) 13
Explanation: For co-primes, LCM = product → 11 × 13.
11. Which number is divisible by 8?
Options: (a) 344 (b) 342 (c) 346 (d) 348
Ans: (a) 344
Explanation: Last three digits 344 ÷ 8 = 43.
12. Find the smallest number that leaves remainder 1 when divided by 2, 3, and 4.
Options: (a) 11 (b) 12 (c) 13 (d) 15
Ans: (c) 13
Explanation: LCM(2,3,4)=12 → 12+1=13.
13. Which is NOT divisible by 11?
Options: (a) 121 (b) 242 (c) 363 (d) 352
Ans: (d) 352
Explanation: Alternating sum rule fails for 352.
14. The product of two numbers is 72 and their HCF is 6. Find the LCM.
Options: (a) 6 (b) 12 (c) 18 (d) 24
Ans: (b) 12
Explanation: Product = HCF × LCM → 72 = 6 × LCM.
15. Which number when divided by 5 and 7 leaves no remainder ?
Options: (a) 30 (b) 35 (c) 40 (d) 45
Ans: (b) 35
Explanation: LCM of 5 and 7 is 35.
16. How many prime numbers are there between 20 and 40 ?
Options: (a) 3 (b) 4 (c) 5 (d) 6
Ans: (b) 4
Explanation: 23, 29, 31, 37.
17. What is the smallest multiple of 15 greater than 200 ?
Options: (a) 210 (b) 215 (c) 220 (d) 225
Ans: (a) 210
Explanation: 15 × 14 = 210.
18. Which number is divisible by 3 but NOT by 9 ?
Options: (a) 18 (b) 27 (c) 36 (d) 24
Ans: (d) 24
Explanation: Digit sum 6 → divisible by 3, not by 9.
19. Find the HCF of 24, 36, and 60.
Options: (a) 6 (b) 12 (c) 18 (d) 24
Ans: (b) 12
Explanation: Highest common factor among all three is 12.
20. The least number that must be added to 567 to make it divisible by 6 is:
Options: (a) 1 (b) 2 (c) 3 (d) 5
Ans: (c) 3
Explanation: 567 ÷ 6 leaves remainder 3 → add 3.