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The HCF of 2410 and 2700 is:
5
1
10
2
10
Use the Euclidean division algorithm: Divide the larger number by the smaller one, then use the remainder to divide the previous divisor until the remainder is zero.
Two numbers are 2410 and 2700.
HCF(a,b)=HCF(b,a(modb))
Use the Euclidean division algorithm: Divide the larger number by the smaller one, then use the remainder to divide the previous divisor until the remainder is zero.
Students often stop too early after the first division; the HCF is the last non-zero divisor, not the last non-zero remainder.
Step 1: Set up the division
Perform the Euclidean division algorithm for 2700 and 2410.
2700=2410├Ч1+290
Step 2: Continue the process
Divide the previous divisor (2410) by the remainder (290).
2410=290├Ч8+90
Step 3: Further reduction
Divide 290 by the new remainder (90).
290=90├Ч3+20
Step 4: Next division
Divide 90 by 20.
90=20├Ч4+10
Step 5: Find the HCF
Divide 20 by 10. Since the remainder is now 0, the last divisor is the HCF.
20=10├Ч2+0
C is correct because the last non-zero divisor in the Euclidean algorithm sequence is 10, which represents the Highest Common Factor.
The HCF is essential for simplifying fractions and solving problems involving the largest possible measure that can divide given quantities exactly.
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