Highest Common Factor of 882, 702, 100 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 882, 702, 100 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 882, 702, 100 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 882, 702, 100 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 882, 702, 100 is 2.
HCF(882, 702, 100) = 2
HCF of 882, 702, 100 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 882, 702, 100 is 2.
Highest Common Factor of 882,702,100 is 2
Step 1: Since 882 > 702, we apply the division lemma to 882 and 702, to get
882 = 702 x 1 + 180
Step 2: Since the reminder 702 ≠ 0, we apply division lemma to 180 and 702, to get
702 = 180 x 3 + 162
Step 3: We consider the new divisor 180 and the new remainder 162, and apply the division lemma to get
180 = 162 x 1 + 18
We consider the new divisor 162 and the new remainder 18, and apply the division lemma to get
162 = 18 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 882 and 702 is 18
Notice that 18 = HCF(162,18) = HCF(180,162) = HCF(702,180) = HCF(882,702) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 100 > 18, we apply the division lemma to 100 and 18, to get
100 = 18 x 5 + 10
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 10 and 18, to get
18 = 10 x 1 + 8
Step 3: We consider the new divisor 10 and the new remainder 8, and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2, and apply the division lemma 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 18 and 100 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(100,18) .
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Frequently Asked Questions on HCF of 882, 702, 100 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 882, 702, 100?
Answer: HCF of 882, 702, 100 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 882, 702, 100 using Euclid's Algorithm?
Answer: For arbitrary numbers 882, 702, 100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.