Two numbers are in the ratio of 15:11. If their HCF is 13, the numbers will be?

HCF and Ratio

The Highest Common Factor (H.C.F) and ratio are two concepts that are closely related and often used together in mathematics. Let’s explore their relationship:

What is HCF?

The Highest Common factor, commonly known as HCF, is defined as the largest positive integer that can divide all the given numbers without leaving any remainder. It represents the highest common divisor among the numbers.

It is a fundamental concept in number theory and plays a crucial role in various mathematical calculations. The HCF can be found using the prime factorization method. By expressing each number as a product of prime factors and identifying the common prime factors, we can determine their HCF.

What is Ratio?

Ratio is a comparison between two quantities or values. It expresses the relationship or proportion between them. Ratios are commonly written in the form of a:b or a/b, where ‘a’ and ‘b’ are the quantities being compared.

Relationship between HCF and Ratio

The relationship between H.C.F and ratio can be understood as follows:

• The H.C.F is the greatest common divisor among the numbers in the ratio.
• It is the largest value that can evenly divide the quantities in the given ratio, without leaving any remainder.

Two Numbers in the Ratio of 15:11 with H.C.F of 13

Let’s consider the required numbers as 15x and 11x

According to the given information, the H.C.F of the numbers is 13. This means that 13 is the highest common factor for both 15x and 11x.

This means that x must equal 13.

So, we substitute the value of x to find the numbers,

15x = 15 x 13 = 195

11x = 11 x 13 = 143

Therefore, the numbers are 195 and 143.

Summary:

Two numbers are in the ratio of 15:11. If their H.C.F is 13, the numbers will be?

When the two numbers are in the ratio of 15:11 and their HCF is 13, the numbers will be 195 and 143. Both Ratio and HCF play a crucial role in various mathematical operations involving ratios, such as simplification, comparison, etc.

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