Highest Common Factor of 946, 7234 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 946, 7234 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 946, 7234 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 946, 7234 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 946, 7234 is 2.
HCF(946, 7234) = 2
HCF of 946, 7234 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 946, 7234 is 2.
Highest Common Factor of 946,7234 is 2
Step 1: Since 7234 > 946, we apply the division lemma to 7234 and 946, to get
7234 = 946 x 7 + 612
Step 2: Since the reminder 946 ≠ 0, we apply division lemma to 612 and 946, to get
946 = 612 x 1 + 334
Step 3: We consider the new divisor 612 and the new remainder 334, and apply the division lemma to get
612 = 334 x 1 + 278
We consider the new divisor 334 and the new remainder 278,and apply the division lemma to get
334 = 278 x 1 + 56
We consider the new divisor 278 and the new remainder 56,and apply the division lemma to get
278 = 56 x 4 + 54
We consider the new divisor 56 and the new remainder 54,and apply the division lemma to get
56 = 54 x 1 + 2
We consider the new divisor 54 and the new remainder 2,and apply the division lemma to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 946 and 7234 is 2
Notice that 2 = HCF(54,2) = HCF(56,54) = HCF(278,56) = HCF(334,278) = HCF(612,334) = HCF(946,612) = HCF(7234,946) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 946, 7234 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 946, 7234?
Answer: HCF of 946, 7234 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 946, 7234 using Euclid's Algorithm?
Answer: For arbitrary numbers 946, 7234 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.