Highest Common Factor of 414, 652, 170, 770 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 414, 652, 170, 770 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 652, 170, 770 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 414, 652, 170, 770 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 414, 652, 170, 770 is 2.
HCF(414, 652, 170, 770) = 2
HCF of 414, 652, 170, 770 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 652, 170, 770 is 2.
Highest Common Factor of 414,652,170,770 is 2
Step 1: Since 652 > 414, we apply the division lemma to 652 and 414, to get
652 = 414 x 1 + 238
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 238 and 414, to get
414 = 238 x 1 + 176
Step 3: We consider the new divisor 238 and the new remainder 176, and apply the division lemma to get
238 = 176 x 1 + 62
We consider the new divisor 176 and the new remainder 62,and apply the division lemma to get
176 = 62 x 2 + 52
We consider the new divisor 62 and the new remainder 52,and apply the division lemma to get
62 = 52 x 1 + 10
We consider the new divisor 52 and the new remainder 10,and apply the division lemma to get
52 = 10 x 5 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 414 and 652 is 2
Notice that 2 = HCF(10,2) = HCF(52,10) = HCF(62,52) = HCF(176,62) = HCF(238,176) = HCF(414,238) = HCF(652,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 170 > 2, we apply the division lemma to 170 and 2, to get
170 = 2 x 85 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 170 is 2
Notice that 2 = HCF(170,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 770 > 2, we apply the division lemma to 770 and 2, to get
770 = 2 x 385 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 770 is 2
Notice that 2 = HCF(770,2) .
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Frequently Asked Questions on HCF of 414, 652, 170, 770 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 414, 652, 170, 770?
Answer: HCF of 414, 652, 170, 770 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 652, 170, 770 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 652, 170, 770 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.