Highest Common Factor of 88, 760, 138 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 88, 760, 138 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 88, 760, 138 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 88, 760, 138 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 88, 760, 138 is 2.
HCF(88, 760, 138) = 2
HCF of 88, 760, 138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 88, 760, 138 is 2.
Highest Common Factor of 88,760,138 is 2
Step 1: Since 760 > 88, we apply the division lemma to 760 and 88, to get
760 = 88 x 8 + 56
Step 2: Since the reminder 88 ≠ 0, we apply division lemma to 56 and 88, to get
88 = 56 x 1 + 32
Step 3: We consider the new divisor 56 and the new remainder 32, and apply the division lemma to get
56 = 32 x 1 + 24
We consider the new divisor 32 and the new remainder 24,and apply the division lemma to get
32 = 24 x 1 + 8
We consider the new divisor 24 and the new remainder 8,and apply the division lemma to get
24 = 8 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 88 and 760 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(56,32) = HCF(88,56) = HCF(760,88) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 138 > 8, we apply the division lemma to 138 and 8, to get
138 = 8 x 17 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 138 is 2
Notice that 2 = HCF(8,2) = HCF(138,8) .
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Frequently Asked Questions on HCF of 88, 760, 138 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 88, 760, 138?
Answer: HCF of 88, 760, 138 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 88, 760, 138 using Euclid's Algorithm?
Answer: For arbitrary numbers 88, 760, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.