Highest Common Factor of 296, 42536 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 296, 42536 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 296, 42536 is 8 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 296, 42536 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 296, 42536 is 8.
HCF(296, 42536) = 8
HCF of 296, 42536 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 296, 42536 is 8.
Highest Common Factor of 296,42536 is 8
Step 1: Since 42536 > 296, we apply the division lemma to 42536 and 296, to get
42536 = 296 x 143 + 208
Step 2: Since the reminder 296 ≠ 0, we apply division lemma to 208 and 296, to get
296 = 208 x 1 + 88
Step 3: We consider the new divisor 208 and the new remainder 88, and apply the division lemma to get
208 = 88 x 2 + 32
We consider the new divisor 88 and the new remainder 32,and apply the division lemma to get
88 = 32 x 2 + 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 296 and 42536 is 8
Notice that 8 = HCF(24,8) = HCF(32,24) = HCF(88,32) = HCF(208,88) = HCF(296,208) = HCF(42536,296) .
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Frequently Asked Questions on HCF of 296, 42536 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 296, 42536?
Answer: HCF of 296, 42536 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 296, 42536 using Euclid's Algorithm?
Answer: For arbitrary numbers 296, 42536 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.