Highest Common Factor of 734, 946, 21 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 734, 946, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 734, 946, 21 is 1 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 734, 946, 21 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 734, 946, 21 is 1.
HCF(734, 946, 21) = 1
HCF of 734, 946, 21 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 734, 946, 21 is 1.
Highest Common Factor of 734,946,21 is 1
Step 1: Since 946 > 734, we apply the division lemma to 946 and 734, to get
946 = 734 x 1 + 212
Step 2: Since the reminder 734 ≠ 0, we apply division lemma to 212 and 734, to get
734 = 212 x 3 + 98
Step 3: We consider the new divisor 212 and the new remainder 98, and apply the division lemma to get
212 = 98 x 2 + 16
We consider the new divisor 98 and the new remainder 16,and apply the division lemma to get
98 = 16 x 6 + 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 734 and 946 is 2
Notice that 2 = HCF(16,2) = HCF(98,16) = HCF(212,98) = HCF(734,212) = HCF(946,734) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 2, we apply the division lemma to 21 and 2, to get
21 = 2 x 10 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 21 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 734, 946, 21 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 734, 946, 21?
Answer: HCF of 734, 946, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 734, 946, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 734, 946, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.