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Answer :
To find the highest common factor (HCF) of 112 and 268 using Euclid's division algorithm, follow these steps:
1. Identify the Larger and Smaller Number:
- Start with the two numbers: 112 and 268.
- Here, 268 is the larger number and 112 is the smaller number.
2. Apply Euclid’s Division Algorithm:
- Divide the larger number by the smaller number and find the remainder.
- Replace the larger number with the smaller number and the smaller number with the remainder.
- Continue this process until the remainder is zero.
3. Step-by-Step Process:
- First Division:
- Divide 268 by 112:
- [tex]\( 268 \div 112 \)[/tex] gives a quotient of 2 and a remainder of 44.
- Second Division:
- Now take 112 (former smaller number) and 44 (remainder), and divide:
- [tex]\( 112 \div 44 \)[/tex] gives a quotient of 2 and a remainder of 24.
- Third Division:
- Now take 44 and 24, and divide:
- [tex]\( 44 \div 24 \)[/tex] gives a quotient of 1 and a remainder of 20.
- Fourth Division:
- Now take 24 and 20, and divide:
- [tex]\( 24 \div 20 \)[/tex] gives a quotient of 1 and a remainder of 4.
- Fifth Division:
- Now take 20 and 4, and divide:
- [tex]\( 20 \div 4 \)[/tex] gives a quotient of 5 and a remainder of 0.
4. Determine the HCF:
- When the remainder becomes 0, the divisor at this step is the HCF.
- In this case, the last non-zero remainder is 4.
Therefore, the HCF of 112 and 268 is 4.
1. Identify the Larger and Smaller Number:
- Start with the two numbers: 112 and 268.
- Here, 268 is the larger number and 112 is the smaller number.
2. Apply Euclid’s Division Algorithm:
- Divide the larger number by the smaller number and find the remainder.
- Replace the larger number with the smaller number and the smaller number with the remainder.
- Continue this process until the remainder is zero.
3. Step-by-Step Process:
- First Division:
- Divide 268 by 112:
- [tex]\( 268 \div 112 \)[/tex] gives a quotient of 2 and a remainder of 44.
- Second Division:
- Now take 112 (former smaller number) and 44 (remainder), and divide:
- [tex]\( 112 \div 44 \)[/tex] gives a quotient of 2 and a remainder of 24.
- Third Division:
- Now take 44 and 24, and divide:
- [tex]\( 44 \div 24 \)[/tex] gives a quotient of 1 and a remainder of 20.
- Fourth Division:
- Now take 24 and 20, and divide:
- [tex]\( 24 \div 20 \)[/tex] gives a quotient of 1 and a remainder of 4.
- Fifth Division:
- Now take 20 and 4, and divide:
- [tex]\( 20 \div 4 \)[/tex] gives a quotient of 5 and a remainder of 0.
4. Determine the HCF:
- When the remainder becomes 0, the divisor at this step is the HCF.
- In this case, the last non-zero remainder is 4.
Therefore, the HCF of 112 and 268 is 4.
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