Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 766, 414, 175 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 766, 414, 175 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 766, 414, 175 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 766, 414, 175 is 1.
HCF(766, 414, 175) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 766, 414, 175 is 1.
Step 1: Since 766 > 414, we apply the division lemma to 766 and 414, to get
766 = 414 x 1 + 352
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 352 and 414, to get
414 = 352 x 1 + 62
Step 3: We consider the new divisor 352 and the new remainder 62, and apply the division lemma to get
352 = 62 x 5 + 42
We consider the new divisor 62 and the new remainder 42,and apply the division lemma to get
62 = 42 x 1 + 20
We consider the new divisor 42 and the new remainder 20,and apply the division lemma to get
42 = 20 x 2 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 766 and 414 is 2
Notice that 2 = HCF(20,2) = HCF(42,20) = HCF(62,42) = HCF(352,62) = HCF(414,352) = HCF(766,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 175 > 2, we apply the division lemma to 175 and 2, to get
175 = 2 x 87 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 175 is 1
Notice that 1 = HCF(2,1) = HCF(175,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 766, 414, 175?
Answer: HCF of 766, 414, 175 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 766, 414, 175 using Euclid's Algorithm?
Answer: For arbitrary numbers 766, 414, 175 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.