Highest Common Factor of 134, 670, 352 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 134, 670, 352 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 134, 670, 352 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 134, 670, 352 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 134, 670, 352 is 2.
HCF(134, 670, 352) = 2
HCF of 134, 670, 352 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 134, 670, 352 is 2.
Highest Common Factor of 134,670,352 is 2
Step 1: Since 670 > 134, we apply the division lemma to 670 and 134, to get
670 = 134 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 134, the HCF of 134 and 670 is 134
Notice that 134 = HCF(670,134) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 352 > 134, we apply the division lemma to 352 and 134, to get
352 = 134 x 2 + 84
Step 2: Since the reminder 134 ≠ 0, we apply division lemma to 84 and 134, to get
134 = 84 x 1 + 50
Step 3: We consider the new divisor 84 and the new remainder 50, and apply the division lemma to get
84 = 50 x 1 + 34
We consider the new divisor 50 and the new remainder 34,and apply the division lemma to get
50 = 34 x 1 + 16
We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get
34 = 16 x 2 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 134 and 352 is 2
Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(50,34) = HCF(84,50) = HCF(134,84) = HCF(352,134) .
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Frequently Asked Questions on HCF of 134, 670, 352 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 134, 670, 352?
Answer: HCF of 134, 670, 352 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 134, 670, 352 using Euclid's Algorithm?
Answer: For arbitrary numbers 134, 670, 352 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.