Advertisements
Advertisements
Question
The product of 2 two digit numbers is 300 and their HCF is 5. What are the numbers?
Advertisements
Solution
Given that HCF of 2 numbers is 5
The numbers may like 5x and 5y
Also given their product = 300
5x × 5y = 300
⇒ 25xy = 300
⇒ xy = `300/25`
⇒ xy = 12
The possible values of x and y be (1, 12) (2, 6) (3, 4)
The numbers will be (5x, 5y)
⇒ (5 × 1, 5 × 12) = (5, 60)
⇒ (5 × 2, 5 × 6) = (10, 30)
⇒ (5 × 3, 5 × 4) = (15, 20)
(5, 60) is impossible because the given the numbers are two digit numbers.
The remaining numbers are (10, 30) and (15, 20)
But given that HCF is 5
(10, 30) is impossible, because its HCF = 10
The numbers are 15, 20
APPEARS IN
RELATED QUESTIONS
Find the HCF of the following number.
81, 99
The number of students of Std 6th and Std 7th who went to visit the Tadoba Tiger Project at Chandrapur was 140 and 196 respectively. The students of each class are to be divided into groups of the same number of students. Each group can have a paid guide. What is the maximum number of students there can be in each group ? Why do you think each group should have the maximum possible number of students?
The HCF of 144 and 198 is ______.
Find the G.C.D for the following:
P5, P11, P9
Find the G.C.D for the following:
9a2b2c3, 15a3b2c4
Find the G.C.D for the following:
ab2c3, a2b3c, a3bc2
Find the G.C.D of the following:
am+1, am+2, am+3
What is the greatest possible volume of a vessel that can be used to measure exactly the volume of milk in cans (in full capacity) of 80 litres, 100 litres and 120 litres?
What is the HCF of two consecutive even numbers?
The length, breadth, and height of a room are 825 cm, 675 cm, and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.
