Highest Common Factor of 565, 974, 178 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 565, 974, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 974, 178 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 565, 974, 178 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 565, 974, 178 is 1.
HCF(565, 974, 178) = 1
HCF of 565, 974, 178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 565, 974, 178 is 1.
Highest Common Factor of 565,974,178 is 1
Step 1: Since 974 > 565, we apply the division lemma to 974 and 565, to get
974 = 565 x 1 + 409
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 409 and 565, to get
565 = 409 x 1 + 156
Step 3: We consider the new divisor 409 and the new remainder 156, and apply the division lemma to get
409 = 156 x 2 + 97
We consider the new divisor 156 and the new remainder 97,and apply the division lemma to get
156 = 97 x 1 + 59
We consider the new divisor 97 and the new remainder 59,and apply the division lemma to get
97 = 59 x 1 + 38
We consider the new divisor 59 and the new remainder 38,and apply the division lemma to get
59 = 38 x 1 + 21
We consider the new divisor 38 and the new remainder 21,and apply the division lemma to get
38 = 21 x 1 + 17
We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get
21 = 17 x 1 + 4
We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get
17 = 4 x 4 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 565 and 974 is 1
Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(38,21) = HCF(59,38) = HCF(97,59) = HCF(156,97) = HCF(409,156) = HCF(565,409) = HCF(974,565) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 178 > 1, we apply the division lemma to 178 and 1, to get
178 = 1 x 178 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 178 is 1
Notice that 1 = HCF(178,1) .
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Frequently Asked Questions on HCF of 565, 974, 178 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 565, 974, 178?
Answer: HCF of 565, 974, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 974, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 974, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.