Highest Common Factor of 678, 964 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 678, 964 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 964 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 678, 964 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 678, 964 is 2.
HCF(678, 964) = 2
HCF of 678, 964 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 964 is 2.
Highest Common Factor of 678,964 is 2
Step 1: Since 964 > 678, we apply the division lemma to 964 and 678, to get
964 = 678 x 1 + 286
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 286 and 678, to get
678 = 286 x 2 + 106
Step 3: We consider the new divisor 286 and the new remainder 106, and apply the division lemma to get
286 = 106 x 2 + 74
We consider the new divisor 106 and the new remainder 74,and apply the division lemma to get
106 = 74 x 1 + 32
We consider the new divisor 74 and the new remainder 32,and apply the division lemma to get
74 = 32 x 2 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 964 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(74,32) = HCF(106,74) = HCF(286,106) = HCF(678,286) = HCF(964,678) .
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Frequently Asked Questions on HCF of 678, 964 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 678, 964?
Answer: HCF of 678, 964 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 964 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.