Highest Common Factor of 768, 970 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 768, 970 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 970 is 2 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 768, 970 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 768, 970 is 2.
HCF(768, 970) = 2
HCF of 768, 970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 970 is 2.
Highest Common Factor of 768,970 is 2
Step 1: Since 970 > 768, we apply the division lemma to 970 and 768, to get
970 = 768 x 1 + 202
Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 202 and 768, to get
768 = 202 x 3 + 162
Step 3: We consider the new divisor 202 and the new remainder 162, and apply the division lemma to get
202 = 162 x 1 + 40
We consider the new divisor 162 and the new remainder 40,and apply the division lemma to get
162 = 40 x 4 + 2
We consider the new divisor 40 and the new remainder 2,and apply the division lemma to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 768 and 970 is 2
Notice that 2 = HCF(40,2) = HCF(162,40) = HCF(202,162) = HCF(768,202) = HCF(970,768) .
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Frequently Asked Questions on HCF of 768, 970 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 768, 970?
Answer: HCF of 768, 970 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 970 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.