Real Numbers MATHS - Real Numbers

A number when divided by 143 leaves 31 as remainder. What will be the remainder when the same number is divided by 13?

2.13113111311113... is:

a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then, the least prime factor of (a + b) is:

What is the largest number that divides 70 and 125, leaving remainders 5 and 8 respectively?

Very-Short-Answer Questions:
State fundamental theorem of arithmatic.

Very-Short-Answer Questions:
Express 360 as product of its prime factors.

Find the greatest possible length which can be used to measure exactly the length 7m, 3m 85cm and 12m 95cm.

Give an example of two irrationals whose sum is rational.

The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other.

Using prime factorization, find the HCF and LCM of:
23, 31

Show that any positive odd integer is of the form (6m + 1) or (6m + 3) or (6m + 5), where m is some integer.

Use Euclid's algorithm to find HCF of 1190 and 1445. express the HCF in the form 1190m + 1445n.

The traffic lights at three different road crossing change after every 48 secons, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 a.m. then at what time will they again change simultaneously?

Find the leash number of square tiles required to pave the ceiling of a room 15m 17cm long and 9m 2cm broad.

Three measuring rods are 64cm, 80cm and 96cm in length. Find the least length of cloth that can be measured an exact number of times, using any of the rods.