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HCF and LCM: Concepts, Methods, and Word Problems

Factors and Multiples A factor of a number divides it exactly without leaving a remainder, while a multiple is obtained by multiplying the number by natural numbers. Every number has 1 as a factor, and its own value as a...

HCF of even prime number and 10 is:

2

The highest common factor of 21 and 90 is:

3

In the following question, a statement of assertion is followed by a statement of reason. Read the given statements carefully and choose the correct option:

Assertion: The HCF of two numbers is 45 and their LCM is 675.

If one number is 135, then the other number is 240.

Reason: The relation between two natural numbers a, b and their HCF and LCM is

a × b = HCF(a, b) × LCM(a, b).

Assertion is false but the reason is true.

If two positive integers x & y are expressible in the form, x = a²b & y = ab², where a, b is prime number, then HCF (x, y) = _________?

ab

What is the condition for a natural number to end with the digit zero?

A natural number ends with the digit zero if and only if its prime factorization contains both 2 and 5.

Define the Highest Common Factor (HCF).

The HCF is the largest number among the common factors of two or more given numbers. It is the largest positive integer that divides two or more integers without leaving a remainder.