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HCF - Word problems

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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HCF (Highest Common Factor) is the largest number that divides two or more given numbers exactly without leaving any remainder.

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In word problems, look for keywords like 'Greatest', 'Maximum', 'Longest', 'Largest', or 'Dividing into equal groups' to identify that you need to find the HCF.

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HCF is also known as GCF (Greatest Common Factor) or GCD (Greatest Common Divisor).

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To find the HCF, list all the factors of the given numbers, identify the common factors, and choose the largest one.

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The HCF of two numbers can never be larger than the smallest of the given numbers.

📐Formulae

HCF=Greatest common factor of the given numbers\text{HCF} = \text{Greatest common factor of the given numbers}

If a÷H=x and b÷H=y (where x,y are integers), then H is a common factor.\text{If } a \div H = x \text{ and } b \div H = y \text{ (where } x, y \text{ are integers), then } H \text{ is a common factor.}

💡Examples

Problem 1:

Two ribbons are 1212 meters and 1818 meters long. They need to be cut into pieces of the same maximum length. What should be the length of each piece?

Solution:

To find the maximum length of each piece, we need to find the HCF of 1212 and 1818. Factors of 1212: 1,2,3,4,6,121, 2, 3, 4, 6, 12 Factors of 1818: 1,2,3,6,9,181, 2, 3, 6, 9, 18 Common Factors: 1,2,3,61, 2, 3, 6 Highest Common Factor (HCF) = 66 So, the length of each piece should be 66 meters.

Explanation:

Since we need the 'maximum' length that divides both 1212 and 1818 perfectly, we calculate the Highest Common Factor.

Problem 2:

A fruit seller has 2424 apples and 3636 oranges. He wants to pack them into boxes such that each box has the same number of fruits and contains only one type of fruit. What is the greatest number of fruits that can be put in each box?

Solution:

We need to find the HCF of 2424 and 3636. Factors of 2424: 1,2,3,4,6,8,12,241, 2, 3, 4, 6, 8, 12, 24 Factors of 3636: 1,2,3,4,6,9,12,18,361, 2, 3, 4, 6, 9, 12, 18, 36 Common Factors: 1,2,3,4,6,121, 2, 3, 4, 6, 12 Highest Common Factor (HCF) = 1212 Therefore, the greatest number of fruits in each box is 1212.

Explanation:

The word 'greatest' indicates that we must find the HCF of the two quantities to divide them into equal maximum-sized groups.

Problem 3:

Find the greatest number that divides 2020 and 3030 without leaving a remainder.

Solution:

We find the factors of 2020 and 3030. Factors of 20={1,2,4,5,10,20}20 = \{1, 2, 4, 5, 10, 20\} Factors of 30={1,2,3,5,6,10,15,30}30 = \{1, 2, 3, 5, 6, 10, 15, 30\} Common Factors = 1,2,5,101, 2, 5, 10 HCF = 1010 The greatest number is 1010.

Explanation:

To divide numbers without a remainder, we look for their factors. To find the 'greatest' such number, we find the HCF.

Word problems Class 4 Notes & Examples | CBSE Maths