Highest Common Factor of 708, 984, 758 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 708, 984, 758 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 984, 758 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 708, 984, 758 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 708, 984, 758 is 2.
HCF(708, 984, 758) = 2
HCF of 708, 984, 758 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 984, 758 is 2.
Highest Common Factor of 708,984,758 is 2
Step 1: Since 984 > 708, we apply the division lemma to 984 and 708, to get
984 = 708 x 1 + 276
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 276 and 708, to get
708 = 276 x 2 + 156
Step 3: We consider the new divisor 276 and the new remainder 156, and apply the division lemma to get
276 = 156 x 1 + 120
We consider the new divisor 156 and the new remainder 120,and apply the division lemma to get
156 = 120 x 1 + 36
We consider the new divisor 120 and the new remainder 36,and apply the division lemma to get
120 = 36 x 3 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 708 and 984 is 12
Notice that 12 = HCF(36,12) = HCF(120,36) = HCF(156,120) = HCF(276,156) = HCF(708,276) = HCF(984,708) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 758 > 12, we apply the division lemma to 758 and 12, to get
758 = 12 x 63 + 2
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 2 and 12, to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 758 is 2
Notice that 2 = HCF(12,2) = HCF(758,12) .
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Frequently Asked Questions on HCF of 708, 984, 758 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 708, 984, 758?
Answer: HCF of 708, 984, 758 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 984, 758 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 984, 758 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.