Highest Common Factor of 352, 870, 74 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 352, 870, 74 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 352, 870, 74 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 352, 870, 74 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 352, 870, 74 is 2.
HCF(352, 870, 74) = 2
HCF of 352, 870, 74 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 352, 870, 74 is 2.
Highest Common Factor of 352,870,74 is 2
Step 1: Since 870 > 352, we apply the division lemma to 870 and 352, to get
870 = 352 x 2 + 166
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 166 and 352, to get
352 = 166 x 2 + 20
Step 3: We consider the new divisor 166 and the new remainder 20, and apply the division lemma to get
166 = 20 x 8 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 352 and 870 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(166,20) = HCF(352,166) = HCF(870,352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 2, we apply the division lemma to 74 and 2, to get
74 = 2 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 74 is 2
Notice that 2 = HCF(74,2) .
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Frequently Asked Questions on HCF of 352, 870, 74 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 352, 870, 74?
Answer: HCF of 352, 870, 74 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 352, 870, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 352, 870, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.