Highest Common Factor of 945, 3521 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 945, 3521 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 945, 3521 is 7 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 945, 3521 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 945, 3521 is 7.
HCF(945, 3521) = 7
HCF of 945, 3521 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 945, 3521 is 7.
Highest Common Factor of 945,3521 is 7
Step 1: Since 3521 > 945, we apply the division lemma to 3521 and 945, to get
3521 = 945 x 3 + 686
Step 2: Since the reminder 945 ≠ 0, we apply division lemma to 686 and 945, to get
945 = 686 x 1 + 259
Step 3: We consider the new divisor 686 and the new remainder 259, and apply the division lemma to get
686 = 259 x 2 + 168
We consider the new divisor 259 and the new remainder 168,and apply the division lemma to get
259 = 168 x 1 + 91
We consider the new divisor 168 and the new remainder 91,and apply the division lemma to get
168 = 91 x 1 + 77
We consider the new divisor 91 and the new remainder 77,and apply the division lemma to get
91 = 77 x 1 + 14
We consider the new divisor 77 and the new remainder 14,and apply the division lemma to get
77 = 14 x 5 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 945 and 3521 is 7
Notice that 7 = HCF(14,7) = HCF(77,14) = HCF(91,77) = HCF(168,91) = HCF(259,168) = HCF(686,259) = HCF(945,686) = HCF(3521,945) .
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Frequently Asked Questions on HCF of 945, 3521 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 945, 3521?
Answer: HCF of 945, 3521 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 945, 3521 using Euclid's Algorithm?
Answer: For arbitrary numbers 945, 3521 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.