Highest Common Factor of 352, 7874 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, 7874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 352, 7874 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, 7874 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, 7874 is 2.
HCF(352, 7874) = 2
HCF of 352, 7874 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, 7874 is 2.
Highest Common Factor of 352,7874 is 2
Step 1: Since 7874 > 352, we apply the division lemma to 7874 and 352, to get
7874 = 352 x 22 + 130
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 130 and 352, to get
352 = 130 x 2 + 92
Step 3: We consider the new divisor 130 and the new remainder 92, and apply the division lemma to get
130 = 92 x 1 + 38
We consider the new divisor 92 and the new remainder 38,and apply the division lemma to get
92 = 38 x 2 + 16
We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get
38 = 16 x 2 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 352 and 7874 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(92,38) = HCF(130,92) = HCF(352,130) = HCF(7874,352) .
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Frequently Asked Questions on HCF of 352, 7874 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, 7874?
Answer: HCF of 352, 7874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 352, 7874 using Euclid's Algorithm?
Answer: For arbitrary numbers 352, 7874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.