If two positive integers a and b are written as a = x3y2 and b = xy2 where x, y are prime numbers, then HCF (a, b) is

By K Balaji|Updated : November 12th, 2022

(a) xy

(b) xy2

(c) x3 y3

(d) x2 y2

 

HCF (a, b) is xy2

Given that, a = x3y2 = x × x × x × y × y

b = xy2 = x × y × y

The product of each common prime facter's smallest power yields the number HCF.

HCF of a and b = HCF (x3y2, xy2) = x × y × y = xy2

Integers

In mathematics, an integer is a grouping of positive and negative numbers. Like whole numbers, integers do not include the fractional component. Therefore, numbers that can be positive, negative, or zero but are not fractions are said to be integers. All mathematical operations, such as addition, subtraction, multiplication, and division, can be performed on integers. Z represents an integer.

Types of Integers

Integers come in three types:

  1. Zero (0) - Zero is not an integer, either positive or negative. There is no (+ or -) sign on zero, making it a neutral number.
  2. Natural Numbers (Positive Integers) - Natural numbers, often known as counting numbers, are positive integers. The symbol Z+ is also used to represent these integers.
  3. The negative of natural numbers are known as negative integers (additive inverse of natural numbers). The symbol for them is Z-. On a number line, the negative integers are located to the left of zero.

Summary:-

If two positive integers a and b are written as a = x3y2 and b = xy2 where x, y are prime numbers, then HCF (a, b) is

If two positive integers a and b are written as a = x3y2 and b = xy2 where x, y are prime numbers, then HCF (a, b) is xy2

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