Question

determine the h.c. f. of the given number by continued division method: 40, 70, and 110​

Answer 1

Answer:

35

Step-by-step explanation:

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

Factors of 175: 1, 5, 7, 25, 35, 175

There are 4 common factors of 70, 105 and 175, that are 1, 35, 5, and 7. Therefore, the highest common factor of 70, 105 and 175 is 35.

F(70, 105, 175) can be thus calculated by first finding HCF(70, 105) using long division and thereafter using this result with 175 to perform long division again.

Step 1: Divide 105 (larger number) by 70 (smaller number).

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (70) by the remainder (35). Repeat this process until the remainder = 0.

⇒ HCF(70, 105) = 35.

Step 3: Now to find the HCF of 35 and 175, we will perform a long division on 175 and 35.

Step 4: For remainder = 0, divisor = 35 ⇒ HCF(35, 175) = 35

Thus, HCF(70, 105, 175) = HCF(HCF(70, 105), 175) = 35.

Answer 2

Answer:

Refer to the attachment.