Highest Common Factor of 112, 756, 69 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 112, 756, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 112, 756, 69 is 1 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 112, 756, 69 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 112, 756, 69 is 1.
HCF(112, 756, 69) = 1
HCF of 112, 756, 69 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 112, 756, 69 is 1.
Highest Common Factor of 112,756,69 is 1
Step 1: Since 756 > 112, we apply the division lemma to 756 and 112, to get
756 = 112 x 6 + 84
Step 2: Since the reminder 112 ≠ 0, we apply division lemma to 84 and 112, to get
112 = 84 x 1 + 28
Step 3: We consider the new divisor 84 and the new remainder 28, and apply the division lemma to get
84 = 28 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 112 and 756 is 28
Notice that 28 = HCF(84,28) = HCF(112,84) = HCF(756,112) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69 > 28, we apply the division lemma to 69 and 28, to get
69 = 28 x 2 + 13
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 13 and 28, to get
28 = 13 x 2 + 2
Step 3: We consider the new divisor 13 and the new remainder 2, and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 28 and 69 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(28,13) = HCF(69,28) .
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Frequently Asked Questions on HCF of 112, 756, 69 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 112, 756, 69?
Answer: HCF of 112, 756, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 112, 756, 69 using Euclid's Algorithm?
Answer: For arbitrary numbers 112, 756, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.