Highest Common Factor of 768, 928, 778 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, 928, 778 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 928, 778 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, 928, 778 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, 928, 778 is 2.
HCF(768, 928, 778) = 2
HCF of 768, 928, 778 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, 928, 778 is 2.
Highest Common Factor of 768,928,778 is 2
Step 1: Since 928 > 768, we apply the division lemma to 928 and 768, to get
928 = 768 x 1 + 160
Step 2: Since the reminder 768 ≠ 0, we apply division lemma to 160 and 768, to get
768 = 160 x 4 + 128
Step 3: We consider the new divisor 160 and the new remainder 128, and apply the division lemma to get
160 = 128 x 1 + 32
We consider the new divisor 128 and the new remainder 32, and apply the division lemma to get
128 = 32 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 768 and 928 is 32
Notice that 32 = HCF(128,32) = HCF(160,128) = HCF(768,160) = HCF(928,768) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 778 > 32, we apply the division lemma to 778 and 32, to get
778 = 32 x 24 + 10
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 10 and 32, to get
32 = 10 x 3 + 2
Step 3: 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 32 and 778 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(778,32) .
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Frequently Asked Questions on HCF of 768, 928, 778 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, 928, 778?
Answer: HCF of 768, 928, 778 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 928, 778 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 928, 778 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.