Question

9. Find the largest number that divides 280 and 490 without leaving a remainder.
bod.
10. Find the smallest number which when divided by 39, 52 and 65 leaves a remainder of
5 in each case.
11. Three tankers contain 140 €, 210 € and 300 l of water. Find the maximum capacity of
the container which can measure the water of the three containers.
12. Find the smallest number, which when divided by 42 and 45 leaves remainders as 6
and 9 respectively.
13. Anita wants to make as many identical rows as possible using 42 red flowers, 63 blue
flowers and 140 yellow flowers. How many rows can she make?
14. A rectangular courtyard is 25 m 35 cm long and 14 m 28 cm broad. It has to be
furnished with square tiles of same size. Find the least possible number of such tiles
required.
HOTS
Six bells start tolling together and toll at the intervals of 3, 6, 9, 12, 15 and 18
seconds respectively. In 30 minutes, how many times will they toll together?
Teacher's Signature
signature
Date
25​

Answer 1

9. We have to determine the largest number that divides 280 and 490 without leaving a remainder. For this, we have to find the H.C.F of these two numbers.

As, H.C.F is the largest positive integer which divides two or more integers without any remainder.

Let us find the factors of 280 and 490

$280 = 2 \times 2 \times 2 \times 5 \times 7$

Now, we will find the factors of 490

$490 = 2 \times 5 \times 7 \times 7$

Hence, the common factors are

$= 2 \times 5 \times 7 = 70$

Therefore, 70 is the largest number which divides 280 and 490 without leaving a remainder.

10. We have to find the smallest number which when divided by 39, 52 and 65

leaves a remainder of 5 in each case. For this first, we have to compute the

L.C.M of 39, 52 and 65

Prime factorization of 39 = 3 × 13

Prime factorization of 52 = 2 × 2 × 13

Prime factorization of 65 = 5 × 13

L.C.M = 2 × 2 × 3 × 5 × 13

L.CM of 39, 52 and 65 = 780

The required smallest number = 780 + 5 = 785

So, the smallest number is 785, which when divided by 39, 52 and 65 leaves a remainder of 5 in each case.

Let us check our answer -

1) 785 ÷ 39

Quotient = 20

Remainder = 5

2) 785 ÷ 52

Quotient = 15

Remainder = 5

3) 785 ÷ 65

Quotient = 12

Remainder = 5

So, when 785 is divided 39, 52 and 65, the remainder is 5 in each case.

11. The maximum capacity of container = H.C.F of ( 140, 210, 300)

Factors of 140 = 1, 2, 4, 5, 7, 10

Factors of 210 = 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 72, 105, 210

Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

H.C.F = 2 × 5 × 10 = 100

Therefore, 100 litres of container is required to measure the quantity.

12. First of all subtract the divisor

42 - 6 = 36

45 - 9 = 36

Smallest number means H.C.F H.C.F of 36 and 36 is 36 therefore, 36 is the smallest number

sorry but 13, 14 and 15 I don't know