Highest Common Factor of 962, 684 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 962, 684 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 962, 684 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 962, 684 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 962, 684 is 2.
HCF(962, 684) = 2
HCF of 962, 684 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 962, 684 is 2.
Highest Common Factor of 962,684 is 2
Step 1: Since 962 > 684, we apply the division lemma to 962 and 684, to get
962 = 684 x 1 + 278
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 278 and 684, to get
684 = 278 x 2 + 128
Step 3: We consider the new divisor 278 and the new remainder 128, and apply the division lemma to get
278 = 128 x 2 + 22
We consider the new divisor 128 and the new remainder 22,and apply the division lemma to get
128 = 22 x 5 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 962 and 684 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(128,22) = HCF(278,128) = HCF(684,278) = HCF(962,684) .
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Frequently Asked Questions on HCF of 962, 684 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 962, 684?
Answer: HCF of 962, 684 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 962, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 962, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.