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 759, 966, 175 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 759, 966, 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 759, 966, 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 759, 966, 175 is 1.
HCF(759, 966, 175) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 759, 966, 175 is 1.
Step 1: Since 966 > 759, we apply the division lemma to 966 and 759, to get
966 = 759 x 1 + 207
Step 2: Since the reminder 759 ≠ 0, we apply division lemma to 207 and 759, to get
759 = 207 x 3 + 138
Step 3: We consider the new divisor 207 and the new remainder 138, and apply the division lemma to get
207 = 138 x 1 + 69
We consider the new divisor 138 and the new remainder 69, and apply the division lemma to get
138 = 69 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 69, the HCF of 759 and 966 is 69
Notice that 69 = HCF(138,69) = HCF(207,138) = HCF(759,207) = HCF(966,759) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 175 > 69, we apply the division lemma to 175 and 69, to get
175 = 69 x 2 + 37
Step 2: Since the reminder 69 ≠ 0, we apply division lemma to 37 and 69, to get
69 = 37 x 1 + 32
Step 3: We consider the new divisor 37 and the new remainder 32, and apply the division lemma to get
37 = 32 x 1 + 5
We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get
32 = 5 x 6 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 69 and 175 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(37,32) = HCF(69,37) = HCF(175,69) .
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 759, 966, 175?
Answer: HCF of 759, 966, 175 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 759, 966, 175 using Euclid's Algorithm?
Answer: For arbitrary numbers 759, 966, 175 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.