Highest Common Factor of 750, 67767 using Euclid's algorithm
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 750, 67767 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 750, 67767 is 3 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 750, 67767 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 750, 67767 is 3.
HCF(750, 67767) = 3
HCF of 750, 67767 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 750, 67767 is 3.
Highest Common Factor of 750,67767 is 3
Step 1: Since 67767 > 750, we apply the division lemma to 67767 and 750, to get
67767 = 750 x 90 + 267
Step 2: Since the reminder 750 ≠ 0, we apply division lemma to 267 and 750, to get
750 = 267 x 2 + 216
Step 3: We consider the new divisor 267 and the new remainder 216, and apply the division lemma to get
267 = 216 x 1 + 51
We consider the new divisor 216 and the new remainder 51,and apply the division lemma to get
216 = 51 x 4 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 750 and 67767 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(216,51) = HCF(267,216) = HCF(750,267) = HCF(67767,750) .
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Frequently Asked Questions on HCF of 750, 67767 using Euclid's Algorithm
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 750, 67767?
Answer: HCF of 750, 67767 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 750, 67767 using Euclid's Algorithm?
Answer: For arbitrary numbers 750, 67767 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.