To find the Highest Common Factor (HCF) of 125 and 165 using the division method, follow these steps:
1. Divide the larger number by the smaller number:
- Here, the larger number is 165, and the smaller number is 125.
- Divide 165 by 125:
[tex]\( 165 \div 125 = 1 \)[/tex] with a remainder of [tex]\( 165 - (125 \times 1) = 40 \)[/tex].
2. Replace the larger number with the smaller number:
- Now, replace 165 with 125 and 125 with the remainder 40.
- So, the new pair of numbers are 125 and 40.
3. Repeat the division:
- Divide 125 by 40:
[tex]\( 125 \div 40 = 3 \)[/tex] with a remainder of [tex]\( 125 - (40 \times 3) = 5 \)[/tex].
4. Replace and divide again:
- Replace 125 with 40 and 40 with the remainder 5.
- So, the new pair of numbers are 40 and 5.
5. Continue the process:
- Divide 40 by 5:
[tex]\( 40 \div 5 = 8 \)[/tex] with a remainder of [tex]\( 40 - (5 \times 8) = 0 \)[/tex].
6. When the remainder is 0:
- The division process stops when the remainder is 0.
- The divisor at this stage is the HCF of the original pair of numbers.
Therefore, the HCF of 125 and 165 is 5.
