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The HCF of 1248 and 2456 is:
8
16
12
14
8
Use the division method: 2456 = 1 × 1248 + 1208; 1248 = 1 × 1208 + 40; 1208 = 30 × 40 + 8; 40 = 5 × 8 + 0. The HCF is the last non-zero divisor.
Two numbers are 1248 and 2456.
HCF(a,b)=HCF(a,b−a) or HCF(b,a)=HCF(a,b(moda))
Use the division method: 2456 = 1 × 1248 + 1208; 1248 = 1 × 1208 + 40; 1208 = 30 × 40 + 8; 40 = 5 × 8 + 0. The HCF is the last non-zero divisor.
Students often stop too early at the first remainder or mistake the division factor with the final divisor.
Set up Euclidean Algorithm
To find the HCF of 1248 and 2456, we divide the larger number by the smaller number to find the remainder.
2456=1248×1+1208
Continue Division
Now, divide the previous divisor (1248) by the remainder (1208).
1248=1208×1+40
Continue Division
Divide the previous divisor (1208) by the new remainder (40).
1208=40×30+8
Final Step
Divide the previous divisor (40) by the remainder (8). The remainder is now 0, so the HCF is the current divisor.
40=8×5+0
A is correct because the HCF obtained through the Euclidean algorithm is 8.
Understanding the Euclidean algorithm is crucial for simplification of large fractions and solving number system problems.
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