Highest Common Factor of 778, 912, 752 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 778, 912, 752 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 778, 912, 752 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 778, 912, 752 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 778, 912, 752 is 2.
HCF(778, 912, 752) = 2
HCF of 778, 912, 752 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 778, 912, 752 is 2.
Highest Common Factor of 778,912,752 is 2
Step 1: Since 912 > 778, we apply the division lemma to 912 and 778, to get
912 = 778 x 1 + 134
Step 2: Since the reminder 778 ≠ 0, we apply division lemma to 134 and 778, to get
778 = 134 x 5 + 108
Step 3: We consider the new divisor 134 and the new remainder 108, and apply the division lemma to get
134 = 108 x 1 + 26
We consider the new divisor 108 and the new remainder 26,and apply the division lemma to get
108 = 26 x 4 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 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 778 and 912 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(108,26) = HCF(134,108) = HCF(778,134) = HCF(912,778) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 752 > 2, we apply the division lemma to 752 and 2, to get
752 = 2 x 376 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 752 is 2
Notice that 2 = HCF(752,2) .
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Frequently Asked Questions on HCF of 778, 912, 752 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 778, 912, 752?
Answer: HCF of 778, 912, 752 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 778, 912, 752 using Euclid's Algorithm?
Answer: For arbitrary numbers 778, 912, 752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.