Highest Common Factor of 946, 205, 169 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 946, 205, 169 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 946, 205, 169 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 946, 205, 169 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 946, 205, 169 is 1.
HCF(946, 205, 169) = 1
HCF of 946, 205, 169 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 946, 205, 169 is 1.
Highest Common Factor of 946,205,169 is 1
Step 1: Since 946 > 205, we apply the division lemma to 946 and 205, to get
946 = 205 x 4 + 126
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 126 and 205, to get
205 = 126 x 1 + 79
Step 3: We consider the new divisor 126 and the new remainder 79, and apply the division lemma to get
126 = 79 x 1 + 47
We consider the new divisor 79 and the new remainder 47,and apply the division lemma to get
79 = 47 x 1 + 32
We consider the new divisor 47 and the new remainder 32,and apply the division lemma to get
47 = 32 x 1 + 15
We consider the new divisor 32 and the new remainder 15,and apply the division lemma to get
32 = 15 x 2 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 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 946 and 205 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(47,32) = HCF(79,47) = HCF(126,79) = HCF(205,126) = HCF(946,205) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 169 > 1, we apply the division lemma to 169 and 1, to get
169 = 1 x 169 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 169 is 1
Notice that 1 = HCF(169,1) .
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Frequently Asked Questions on HCF of 946, 205, 169 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 946, 205, 169?
Answer: HCF of 946, 205, 169 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 946, 205, 169 using Euclid's Algorithm?
Answer: For arbitrary numbers 946, 205, 169 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.